System and method for applying orthogonal limitations to light beams using microelectromechanical systems

ABSTRACT

A system for generating a light beam having a plurality of orthogonal function modes includes a light source for generating a plane wave light beam. A MicroElectroMechanical (MEM) system including an array of micro-mirrors for generating the light beam having the plurality of orthogonal function modes applied thereto responsive to the plane wave light beam and control signals for controlling the array of micro-mirrors. A controller generates the control signals to control a position of each of a plurality of micro-mirrors of the array of micro-mirrors. The controller controls the position of the micro-mirrors to generate a plurality of holograms for applying the plurality of orbital angular momentum modes to the plane wave light beam responsive to the control signals.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. Provisional Application No.62/056,227, filed Sep. 26, 2014, entitled ORBITAL ANGULAR MOMENTUM USINGMEMS (Atty. Dkt. No. NXGN-32363), which is incorporated by referenceherein in its entirety.

This application is also a Continuation-in-Part of U.S. patentapplication Ser. No. 14/731,191, filed Jun. 4, 2015, entitled SYSTEMSAND METHODS FOR FOCUSING BEAMS WITH MODE DIVISION MULTIPLEXING (Atty.Dkt. No. NXGN-32372), which claims benefit of U.S. ProvisionalApplication No. 62/035,224, filed Aug. 8, 2014, entitled FOCUSINGAPPROACH FOR OAM-BASED FREE-SPACE AND RF (Atty. Dkt. No. NXGN-32317).U.S. patent application Ser. No. 14/731,191 and 62/035,224 areincorporated by reference herein in their entirety.

TECHNICAL FIELD

The following relates to orthogonal function based opticalcommunication, and more particularly, to the generation of orthogonalfunction signals within an optical signal using micro electromechanicalsystems.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding, reference is now made to thefollowing description taken in conjunction with the accompanyingDrawings in which:

FIG. 1 illustrates a general overview of the manner for providingcommunication bandwidth between various communication protocolinterfaces;

FIG. 2 illustrates the manner for utilizing multiple level overlaymodulation with twisted pair/cable interfaces;

FIG. 3 illustrates a general block diagram for processing a plurality ofdata streams within an optical communication system;

FIG. 4 is a functional block diagram of a system for generating orbitalangular momentum within a communication system;

FIG. 5 is a functional block diagram of the orbital angular momentumsignal processing block of FIG. 4;

FIG. 6 is a functional block diagram illustrating the manner forremoving orbital angular momentum from a received signal including aplurality of data streams;

FIG. 7 illustrates a single wavelength having two quanti-spinpolarizations providing an infinite number of signals having variousorbital angular momentums associated therewith;

FIG. 8A illustrates an object with only a spin angular momentum;

FIG. 8B illustrates an object with an orbital angular momentum;

FIG. 8C illustrates a circularly polarized beam carrying spin angularmomentum;

FIG. 8D illustrates the phase structure of a light beam carrying anorbital angular momentum;

FIG. 9A illustrates a plane wave having only variations in the spinangular momentum;

FIG. 9B illustrates a signal having both spin and orbital angularmomentum applied thereto;

FIGS. 10A-10C illustrate various signals having different orbitalangular momentum applied thereto;

FIG. 10D illustrates a propagation of Poynting vectors for various Eigenmodes;

FIG. 10E illustrates a spiral phase plate;

FIG. 11 illustrates a typical OAM multiplexing scheme;

FIG. 12 illustrates various manners for converting a Gaussian beam intoan OAM beam;

FIG. 13A illustrates spatial multiplexing using cascaded beam splitters;

FIG. 13B illustrated demultiplexing using cascaded beam splitters andconjugated spiral phase holograms;

FIG. 14 illustrates a log polar geometrical transformation based on OAMmultiplexing and demultiplexing;

FIG. 15A illustrates an intensity profile of generated OAM beams andtheir multiplexing;

FIG. 15B illustrates the optical spectrum of each channel after eachmultiplexing for the OAM beams of FIG. 10A;

FIG. 15C illustrates the recovered constellations of 16-QAM signalscarried on each OAM beam;

FIG. 16A illustrates the steps to produce 24 multiplex OAM beams;

FIG. 16B illustrates the optical spectrum of a WDM signal carrier on anOAM beam;

FIG. 17A illustrates a turbulence emulator;

FIG. 17B illustrates the measured power distribution of an OAM beamafter passing through turbulence with a different strength;

FIG. 18A illustrates how turbulence effects mitigation using adaptiveoptics;

FIG. 18B illustrates experimental results of distortion mitigation usingadaptive optics;

FIG. 19 illustrates a free-space optical data link using OAM;

FIG. 20A illustrates simulated spot sized of different orders of OAMbeams as a function of transmission distance for a 3 cm transmittedbeam;

FIG. 20B illustrates simulated power loss as a function of aperturesize;

FIG. 21A illustrates a perfectly aligned system between a transmitterand receiver;

FIG. 21B illustrates a system with lateral displacement of alignmentbetween a transmitter and receiver;

FIG. 21C illustrates a system with receiver angular error for alignmentbetween a transmitter and receiver;

FIG. 22A illustrates simulated power distribution among different OAMmodes with a function of lateral displacement;

FIG. 22B illustrates simulated power distribution among different OAMmodes as a function of receiver angular error;

FIG. 23 illustrates a free-space communication system;

FIG. 24 illustrates a block diagram of a free-space optics system usingorbital angular momentum and multi-level overlay modulation;

FIGS. 25A-25C illustrate the manner for multiplexing multiple datachannels into optical links to achieve higher data capacity;

FIG. 25D illustrates groups of concentric rings for a wavelength havingmultiple OAM valves;

FIG. 26 illustrates a WDM channel containing many orthogonal OAM beams;

FIG. 27 illustrates a node of a free-space optical system;

FIG. 28 illustrates a network of nodes within a free-space opticalsystem;

FIG. 29 illustrates a system for multiplexing between a free spacesignal and an RF signal;

FIG. 30 illustrates the manner for generating a light beam includingorthogonal functions;

FIGS. 31A-31H illustrate holograms that may be used for modulating abeam;

FIG. 32A is a block diagram of a digital micro-mirror device;

FIG. 32B illustrates the manner in which a micro-mirror interacts with alight source;

FIG. 33 illustrates the mechanical structure of the micro-mirror;

FIG. 34 is a block diagram of the functional components of amicro-mirror;

FIG. 35 illustrates a flow chart of the process for changing theposition of a micro-mirror;

FIG. 36 illustrates an intensity in phase interferometer for measuringthe intensity and phase of a generated beam;

FIG. 37 illustrates the manner in which switching between different OAMmodes may be achieved in real time;

FIG. 38 illustrates the window transmission curves for Corning 7056;

FIGS. 39-43 are zoomed in views of visible and UV AR coated windowtransmittance for Corning 7056;

FIG. 44 illustrates circuitry for the generation of an OAM twisted beamusing a hologram within a micro-electromechanical device;

FIG. 45 illustrates multiple holograms generated by amicro-electromechanical device;

FIG. 46 illustrates a square array of holograms on a dark background;

FIG. 47 illustrates a hexagonal array of holograms on a dark background;

FIG. 48 illustrates a process for multiplexing various OAM modestogether;

FIG. 49 illustrates fractional binary fork holograms;

FIG. 50 illustrates an array of square holograms with no separation on alight background and associated generated OAM mode image;

FIG. 51 illustrates an array of circular holograms separated on a lightbackground and associated generated OAM mode image;

FIG. 52 illustrates an array of square holograms with no separation on adark background and associated generated OAM mode image;

FIG. 53 illustrates an array of circular holograms on a dark backgroundand associated generated OAM mode image;

FIG. 54 illustrates circular holograms with separation on a brightbackground and associated generated OAM mode image;

FIG. 55 illustrates circular holograms with separation on a darkbackground and associated generated OAM mode image;

FIG. 56 illustrates a hexagonal array of circular holograms on a brightbackground and associated OAM mode image;

FIG. 57 illustrates an hexagonal array of small holograms on a brightbackground and associated OAM mode image;

FIG. 58 illustrates a hexagonal array of circular holograms on a darkbackground and associated OAM mode image;

FIG. 59 illustrates a hexagonal array of small holograms on a darkbackground and associated OAM mode image;

FIG. 60 illustrates a hexagonal array of small holograms separated on adark background and associated OAM mode image;

FIG. 61 illustrates a hexagonal array of small holograms closely locatedon a dark background and associated OAM mode image;

FIG. 62 illustrates a hexagonal array of small holograms that areseparated on a bright background and associated OAM mode image;

FIG. 63 illustrates a hexagonal array of small holograms that areclosely located on a bright background and associated OAM mode image;

FIG. 64 illustrates reduced binary holograms having a radius equal to100 micro-mirrors and a period of 50 for various OAM modes;

FIG. 65 illustrates OAM modes for holograms having a radius of 50micro-mirrors and a period of 50;

FIG. 66 illustrates OAM modes for holograms having a radius of 100micro-mirrors and a period of 100;

FIG. 67 illustrates OAM modes for holograms having a radius of 50micro-mirrors and a period of 50;

FIG. 68 illustrates additional methods of multimode OAM generation byimplementing multiple holograms within a MEMs device; and

FIG. 69 illustrates binary spiral holograms.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like reference numbers are usedherein to designate like elements throughout, the various views andembodiments of system and method for communication using orbital angularmomentum with modulation are illustrated and described, and otherpossible embodiments are described. The figures are not necessarilydrawn to scale, and in some instances the drawings have been exaggeratedand/or simplified in places for illustrative purposes only. One ofordinary skill in the art will appreciate the many possible applicationsand variations based on the following examples of possible embodiments.

Referring now to the drawings, and more particularly to FIG. 1, there isillustrated a general overview of the manner for providing improvedspectral efficiency within various communication protocol interfaces102, using a combination of multiple level overlay modulation 104 andthe application of orbital angular momentum 106 to increase the numberof communications channels.

The various communication protocol interfaces 102 may be comprised of avariety of system links using the electromagnetic spectrum, such as RF,cable or twisted pair, or optical making use of light wavelengths suchas fiber-optic communications or free-space optics. Various types of RFcommunications may include a combination of RF microwave, RF satellitecommunication, nomadic and mobile wireless systems, as well asmultiplexing between RF and free-space optics in real time.

By combining a multiple layer overlay modulation technique 104 withorbital angular momentum (OAM) technique 106, a higher throughput overvarious types of system 102 may be achieved. The use of multiple leveloverlay modulation alone without OAM increases the spectral efficiencyof systems 102, whether wired, optical, or wireless. However, togetherwith OAM, the increase in spectral efficiency is even more significant.

Multiple overlay modulation techniques 104 provide a new degree offreedom beyond the conventional 2 degrees of freedom, with time T andfrequency F being independent variables in a two-dimensional notationalspace defining orthogonal axes in an information diagram. This comprisesa more general approach rather than modeling signals as fixed in eitherthe frequency or time domain. Previous modeling methods using fixed timeor fixed frequency are considered to be more limiting cases of thegeneral approach of using multiple level overlay modulation 104. Withinthe multiple level overlay modulation technique 104, signals may bedifferentiated in two-dimensional space rather than along a single axis.Thus, the information-carrying capacity and/or spectral efficiency of asystem may be determined by a number of signals which occupy differenttime and frequency coordinates and may be differentiated in a notationaltwo-dimensional space.

Within the notational two-dimensional space, minimization of the timebandwidth product, i.e., the area occupied by a signal in that space,enables denser packing, and thus, the use of more signals, with higherresulting information-carrying capacity and/or spectral efficiency,within a fixed bandwidth. Given the frequency bandwidth delta (Δf), agiven signal transmitted through it in minimum time Δt will have anenvelope described by certain time-bandwidth minimizing signals. Thetime-bandwidth products for these signals take the form;

ΔtΔf=½(2n+1)  (1)

where n is an integer ranging from 0 to infinity, denoting the order ofthe signal.

These signals form an orthogonal set of infinite elements, where eachhas a finite amount of energy. They are finite in both the time domainand the frequency domain, and can be detected from a mix of othersignals and noise through correlation, for example, by match filtering.Unlike other wavelets, these orthogonal signals have similar time andfrequency forms.

The orbital angular momentum process 106 provides a twist to wave frontsof the electromagnetic fields carrying the data stream that may enablethe transmission of multiple data streams on the same frequency,wavelength, or other signal-supporting mechanism. This will increase thebandwidth over a system by allowing a single frequency or wavelength tosupport multiple eigen channels, each of the individual channels havinga different orthogonal and independent orbital angular momentumassociated therewith.

In one embodiment, referring now to FIG. 2, there is illustrated afurther communication implementation technique using the above describedtechniques as twisted pairs or cables carry electrons (not photons).Rather than using each of the multiple level overlay modulation 104 andorbital angular momentum techniques 106, only the multiple level overlaymodulation 104 can be used in conjunction with a single wirelineinterface and, more particularly, a twisted pair communication link or acable communication link 202. The operation of the multiple leveloverlay modulation 204, is similar to that discussed previously withrespect to FIG. 1, but is used by itself without the use of orbitalangular momentum techniques 106, and is used with either a twisted paircommunication link or cable interface communication link 202.

Referring now to FIG. 3, there is illustrated a general block diagramfor processing a plurality of data streams 302 for transmission in anoptical communication system. The multiple data streams 302 are providedto the multi-layer overlay modulation circuitry 304 wherein the signalsare modulated using the multi-layer overlay modulation technique. Themodulated signals are provided to orbital angular momentum processingcircuitry 306 which applies a twist to each of the wave fronts beingtransmitted on the wavelengths of the optical communication channel. Thetwisted waves are transmitted through the optical interface 308 over anoptical communications link such as an optical fiber or free spaceoptics communication system. FIG. 3 may also illustrate an RF mechanismwherein the interface 308 would comprise and RF interface rather than anoptical interface.

Referring now more particularly to FIG. 4, there is illustrated afunctional block diagram of a system for generating the orbital angularmomentum “twist” within a communication system, such as that illustratedwith respect to FIG. 1, to provide a data stream that may be combinedwith multiple other data streams for transmission upon a same wavelengthor frequency. Multiple data streams 402 are provided to the transmissionprocessing circuitry 400. Each of the data streams 402 comprises, forexample, an end to end connection carrying a voice call or a packetconnection transmitting non-circuit switch packed data over a dataconnection. The multiple data streams 402 are processed bymodulator/demodulator circuitry 404. The modulator/demodulator circuitry404 modulates the received data stream 402 onto a wavelength orfrequency channel using a multiple level overlay modulation technique,as will be more fully described herein below. The communications linkmay comprise an optical fiber link, free-space optics link, RF microwavelink, RF satellite link, wired link (without the twist), etc.

The modulated data stream is provided to the orbital angular momentum(OAM) signal processing block 406. Each of the modulated data streamsfrom the modulator/demodulator 404 are provided a different orbitalangular momentum by the orbital angular momentum electromagnetic block406 such that each of the modulated data streams have a unique anddifferent orbital angular momentum associated therewith. Each of themodulated signals having an associated orbital angular momentum areprovided to an optical transmitter 408 that transmits each of themodulated data streams having a unique orbital angular momentum on asame wavelength. Each wavelength has a selected number of bandwidthslots B and may have its data transmission capability increase by afactor of the number of degrees of orbital angular momentum l that areprovided from the OAM electromagnetic block 406. The optical transmitter408 transmitting signals at a single wavelength could transmit B groupsof information. The optical transmitter 408 and OAM electromagneticblock 406 may transmit l×B groups of information according to theconfiguration described herein.

In a receiving mode, the optical transmitter 408 will have a wavelengthincluding multiple signals transmitted therein having different orbitalangular momentum signals embedded therein. The optical transmitter 408forwards these signals to the OAM signal processing block 406, whichseparates each of the signals having different orbital angular momentumand provides the separated signals to the demodulator circuitry 404. Thedemodulation process extracts the data streams 402 from the modulatedsignals and provides it at the receiving end using the multiple layeroverlay demodulation technique.

Referring now to FIG. 5, there is provided a more detailed functionaldescription of the OAM signal processing block 406. Each of the inputdata streams are provided to OAM circuitry 502. Each of the OAMcircuitry 502 provides a different orbital angular momentum to thereceived data stream. The different orbital angular momentums areachieved by applying different currents for the generation of thesignals that are being transmitted to create a particular orbitalangular momentum associated therewith. The orbital angular momentumprovided by each of the OAM circuitries 502 are unique to the datastream that is provided thereto. An infinite number of orbital angularmomentums may be applied to different input data streams using manydifferent currents. Each of the separately generated data streams areprovided to a signal combiner 504, which combines the signals onto awavelength for transmission from the transmitter 506.

Referring now to FIG. 6, there is illustrated an embodiment in which theOAM processing circuitry 406 may separate a received signal intomultiple data streams. The receiver 602 receives the combined OAMsignals on a single wavelength and provides this information to a signalseparator 604. The signal separator 604 separates each of the signalshaving different orbital angular momentums from the received wavelengthand provides the separated signals to OAM de-twisting circuitry 606. TheOAM de-twisting circuitry 606 removes the associated OAM twist from eachof the associated signals and provides the received modulated datastream for further processing. The signal separator 604 separates eachof the received signals that have had the orbital angular momentumremoved therefrom into individual received signals. The individuallyreceived signals are provided to the receiver 602 for demodulationusing, for example, multiple level overlay demodulation as will be morefully described herein below.

FIG. 7 illustrates in a manner in which a single wavelength orfrequency, having two quanti-spin polarizations may provide an infinitenumber of twists having various orbital angular momentums associatedtherewith. The l axis represents the various quantized orbital angularmomentum states which may be applied to a particular signal at aselected frequency or wavelength. The symbol omega (ω) represents thevarious frequencies to which the signals of differing orbital angularmomentum may be applied. The top grid 702 represents the potentiallyavailable signals for a left handed signal polarization, while thebottom grid 704 is for potentially available signals having right handedpolarization.

By applying different orbital angular momentum states to a signal at aparticular frequency or wavelength, a potentially infinite number ofstates may be provided at the frequency or wavelength. Thus, the stateat the frequency Δω or wavelength 706 in both the left handedpolarization plane 702 and the right handed polarization plane 704 canprovide an infinite number of signals at different orbital angularmomentum states Δl. Blocks 708 and 710 represent a particular signalhaving an orbital angular momentum Δl at a frequency Δω or wavelength inboth the right handed polarization plane 704 and left handedpolarization plane 710, respectively. By changing to a different orbitalangular momentum within the same frequency Δψ or wavelength 706,different signals may also be transmitted. Each angular momentum statecorresponds to a different determined current level for transmissionfrom the optical transmitter. By estimating the equivalent current forgenerating a particular orbital angular momentum within the opticaldomain and applying this current for transmission of the signals, thetransmission of the signal may be achieved at a desired orbital angularmomentum state.

Thus, the illustration of FIG. 7, illustrates two possible angularmomentums, the spin angular momentum, and the orbital angular momentum.The spin version is manifested within the polarizations of macroscopicelectromagnetism, and has only left and right hand polarizations due toup and down spin directions. However, the orbital angular momentumindicates an infinite number of states that are quantized. The paths aremore than two and can theoretically be infinite through the quantizedorbital angular momentum levels.

It is well-known that the concept of linear momentum is usuallyassociated with objects moving in a straight line. The object could alsocarry angular momentum if it has a rotational motion, such as spinning(i.e., spin angular momentum (SAM) 802), or orbiting around an axis 806(i.e., OAM 804), as shown in FIGS. 8A and 8B, respectively. A light beammay also have rotational motion as it propagates. In paraxialapproximation, a light beam carries SAM 802 if the electrical fieldrotates along the beam axis 806 (i.e., circularly polarized light 805),and carries OAM 804 if the wave vector spirals around the beam axis 806,leading to a helical phase front 808, as shown in FIGS. 8C and 8D. Inits analytical expression, this helical phase front 808 is usuallyrelated to a phase term of exp(ilθ) in the transverse plane, where θrefers to the angular coordinate, and l is an integer indicating thenumber of intertwined helices (i.e., the number of 2π phase shifts alongthe circle around the beam axis). l could be a positive, negativeinteger or zero, corresponding to clockwise, counterclockwise phasehelices or a Gaussian beam with no helix, respectively.

Two important concepts relating to OAM include:

1) OAM and polarization: As mentioned above, an OAM beam is manifestedas a beam with a helical phase front and therefore a twistingwavevector, while polarization states can only be connected to SAM 802.A light beam carries SAM 802 of ±h/2π (h is Plank's constant) per photonif it is left or right circularly polarized, and carries no SAM 802 ifit is linearly polarized. Although the SAM 802 and OAM 804 of light canbe coupled to each other under certain scenarios, they can be clearlydistinguished for a paraxial light beam. Therefore, with the paraxialassumption, OAM 804 and polarization can be considered as twoindependent properties of light.

2) OAM beam and Laguerre-Gaussian (LG) beam: In general, an OAM-carryingbeam could refer to any helically phased light beam, irrespective of itsradial distribution (although sometimes OAM could also be carried by anon-helically phased beam). LG beam is a special subset among allOAM-carrying beams, due to that the analytical expression of LG beamsare eigen-solutions of paraxial form of the wave equation in acylindrical coordinates. For an LG beam, both azimuthal and radialwavefront distributions are well defined, and are indicated by two indexnumbers, l and p, of which l has the same meaning as that of a generalOAM beam, and p refers to the radial nodes in the intensitydistribution. Mathematical expressions of LG beams form an orthogonaland complete basis in the spatial domain. In contrast, a general OAMbeam actually comprises a group of LG beams (each with the same l indexbut a different p index) due to the absence of radial definition. Theterm of “OAM beam” refers to all helically phased beams, and is used todistinguish from LG beams.

Using the orbital angular momentum state of the transmitted energysignals, physical information can be embedded within the radiationtransmitted by the signals. The Maxwell-Heaviside equations can berepresented as:

$\begin{matrix}{{{\nabla{\cdot E}} = \frac{\rho}{ɛ_{0}}}{{\nabla{\times E}} = {- \frac{\partial B}{\partial t}}}{{\nabla{\cdot B}} = 0}{{\nabla{\times B}} = {{ɛ_{0}\mu_{0}\frac{\partial E}{\partial t}} + {\mu_{0}{j( {t,x} )}}}}} & (2)\end{matrix}$

where ∇ is the del operator, E is the electric field intensity and B isthe magnetic flux density. Using these equations, one can derive 23symmetries/conserved quantities from Maxwell's original equations.However, there are only ten well-known conserved quantities and only afew of these are commercially used. Historically if Maxwell's equationswhere kept in their original quaternion forms, it would have been easierto see the symmetries/conserved quantities, but when they were modifiedto their present vectorial form by Heaviside, it became more difficultto see such inherent symmetries in Maxwell's equations.

The conserved quantities and the electromagnetic field can berepresented according to the conservation of system energy and theconservation of system linear momentum. Time symmetry, i.e. theconservation of system energy can be represented using Poynting'stheorem according to the equations:

$H = {{\sum\limits_{i}{m_{i}\gamma_{i}c^{2}}} + {\frac{ɛ_{0}}{2}{\int{^{3}{x( {{E}^{2} + {c^{2}{B}^{2}}} )}}}}}$Hamiltonian  (total  energy)${\frac{U^{mech}}{t} + \frac{U^{em}}{t} + {\oint_{s^{\prime}}{{^{2}x^{\prime}}{{\hat{n}}^{\prime} \cdot S}}}} = 0$conservation  of  energy

The space symmetry, i.e., the conservation of system linear momentumrepresenting the electromagnetic Doppler shift can be represented by theequations:

$p = {{\sum\limits_{i}{m_{i}\gamma_{i}v_{i}}} + {ɛ_{0}{\int{^{3}{x( {E \times B} )}}}}}$linear  momentum${\frac{p^{mech}}{t} + \frac{p^{em}}{t} + {\oint_{s^{\prime}}{{^{2}x^{\prime}}{{\hat{n}}^{\prime} \cdot T}}}} = 0$conservation  of  linear  momentum

The conservation of system center of energy is represented by theequation:

$\begin{matrix}{R = {{\frac{1}{H}{\sum\limits_{i}{( {x_{i} - x_{0}} )m_{i}\gamma_{i}c^{2}}}} + {\frac{ɛ_{0}}{2H}{\int{{^{3}{x( {x - x_{0}} )}}( {{E^{2}} + {c^{2}{B^{2}}}} )}}}}} & (3)\end{matrix}$

Similarly, the conservation of system angular momentum, which gives riseto the azimuthal Doppler shift is represented by the equation:

${\frac{J^{mech}}{t} + \frac{J^{em}}{t} + {\oint_{s^{\prime}}{{^{2}x^{\prime}}{{\hat{n}}^{\prime} \cdot M}}}} = 0$conservation  of  angular  momentum

For radiation beams in free space, the EM field angular momentum J^(em)can be separated into two parts:

J ^(em)=ε₀∫_(V′) d ³ x′(E×A)+ε₀∫_(V′) d ³ x′E _(i)[(x′−x ₀)×∇]A_(i)  (4)

For each singular Fourier mode in real valued representation:

$\begin{matrix}{J^{em} = {{{- }\; \frac{ɛ_{0}}{2\omega}{\int_{V^{\prime}}{^{3}{x^{\prime}( {E^{*} \times E} )}}}} - {\; \frac{ɛ_{0}}{2\omega}{\int_{V^{\prime}}{{^{3}x^{\prime}}{E_{i}\lbrack {( {x^{\prime} - x_{0}} ) \times \nabla} \rbrack}E_{i}}}}}} & (5)\end{matrix}$

The first part is the EM spin angular momentum S^(em), its classicalmanifestation is wave polarization. And the second part is the EMorbital angular momentum L^(em) its classical manifestation is wavehelicity. In general, both EM linear momentum P^(em), and EM angularmomentum J^(em)=L^(em)+S^(em) are radiated all the way to the far field.

By using Poynting theorem, the optical vorticity of the signals may bedetermined according to the optical velocity equation:

${{\frac{\partial U}{\partial t} + {\nabla{\cdot S}}} = 0},{{continuity}\mspace{14mu} {equation}}$

where S is the Poynting vector

S=1/4(E×H*+E*×H),  (6)

and U is the energy density

U=1/4(ε|E| ²+μ₀ |H| ²),  (7)

with E and H comprising the electric field and the magnetic field,respectively, and ε and μ₀ being the permittivity and the permeabilityof the medium, respectively. The optical voracity V may then bedetermined by the curl of the optical velocity according to theequation:

$\begin{matrix}{V = {{\nabla{\times v_{opt}}} = {\nabla{\times ( \frac{{E \times H^{*}} + {E^{*} \times H}}{{ɛ{E}^{2}} + {\mu_{0}{H}^{2}}} )}}}} & (8)\end{matrix}$

Referring now to FIGS. 9A and 9B, there is illustrated the manner inwhich a signal and its associated Poynting vector in a plane wavesituation. In the plane wave situation illustrated generally at 902, thetransmitted signal may take one of three configurations. When theelectric field vectors are in the same direction, a linear signal isprovided, as illustrated generally at 904. Within a circularpolarization 906, the electric field vectors rotate with the samemagnitude. Within the elliptical polarization 908, the electric fieldvectors rotate but have differing magnitudes. The Poynting vectorremains in a constant direction for the signal configuration to FIG. 9Aand always perpendicular to the electric and magnetic fields. Referringnow to FIG. 9B, when a unique orbital angular momentum is applied to asignal as described here and above, the Poynting vector S 910 willspiral about the direction of propagation of the signal. This spiral maybe varied in order to enable signals to be transmitted on the samefrequency as described herein.

FIGS. 12A-12C illustrate the differences in signals having differenthelicity (i.e., orbital angular momentums). Each of the spiralingPoynting vectors associated with the signals 902, 904, and 906 provide adifferent shaped signal. Signal 1202 has an orbital angular momentum of+1, signal 1204 has an orbital angular momentum of +3, and signal 1206has an orbital angular momentum of −4. Each signal has a distinctangular momentum and associated Poynting vector enabling the signal tobe distinguished from other signals within a same frequency. This allowsdiffering type of information to be combined on the same frequency,since these signals are separately detectable and do not interfere witheach other (Eigen channels).

FIG. 12D illustrates the propagation of Poynting vectors for variousEigen modes. Each of the rings 1220 represents a different Eigen mode ortwist representing a different orbital angular momentum within the samefrequency. Each of these rings 1220 represents a different orthogonalchannel. Each of the Eigen modes has a Poynting vector 1222 associatedtherewith.

Topological charge may be multiplexed to the frequency for either linearor circular polarization. In case of linear polarizations, topologicalcharge would be multiplexed on vertical and horizontal polarization. Incase of circular polarization, topological charge would multiplex onleft hand and right hand circular polarizations. The topological chargeis another name for the helicity index “I” or the amount of twist or OAMapplied to the signal. The helicity index may be positive or negative.In RF, different topological charges can be created and muxed togetherand de-muxed to separate the topological charges.

The topological charges ls can be created using Spiral Phase Plates(SPPs) as shown in FIG. 9E using a proper material with specific indexof refraction and ability to machine shop or phase mask, hologramscreated of new materials or a new technique to create an RF version ofSpatial Light Modulator (SLM) that does the twist of the RF waves (asopposed to optical beams) by adjusting voltages on the device resultingin twisting of the RF waves with a specific topological charge. SpiralPhase plates can transform a RF plane wave (l=0) to a twisted RF wave ofa specific helicity (i.e. l=+1).

These embodiments can create cross talk and multipath interference.However, cross talk and multipath interference can be corrected using RFMultiple-Input-Multiple-Output (MIMO). In one embodiment, most of thechannel impairments can be detected using a control or pilot channel andbe corrected using algorithmic techniques (closed loop control system).However, other techniques can be used to eliminate these channelimpairments.

As described previously with respect to FIG. 3, each of the multipledata streams applied within the processing circuitry has a multiplelayer overlay modulation scheme applied thereto.

Application of OAM to Optical Communication

Utilization of OAM for optical communications is based on the fact thatcoaxially propagating light beams with different OAM states can beefficiently separated. This is certainly true for orthogonal modes suchas the LG beam. Interestingly, it is also true for general OAM beamswith cylindrical symmetry by relying only on the azimuthal phase.Considering any two OAM beams with an azimuthal index of l1 and l2,respectively:

U ₁(r,θ,z)=A ₁(r,z)exp(il ₁θ)  (12)

where r and z refers to the radial position and propagation distancerespectively, one can quickly conclude that these two beams areorthogonal in the sense that:

$\begin{matrix}{{\int_{0}^{2\pi}{U_{1}U_{2}^{*}{\theta}}} = \{ \begin{matrix}0 & {{{if}\mspace{14mu} _{1}} \neq _{2}} \\{A_{1}A_{2}^{*}} & {{{if}\mspace{14mu} _{1}} = _{2}}\end{matrix} } & (13)\end{matrix}$

There are two different ways to take advantage of the distinctionbetween OAM beams with different l states in communications. In thefirst approach, N different OAM states can be encoded as N differentdata symbols representing “0”, “1”, . . . , “N−1”, respectively. Asequence of OAM states sent by the transmitter therefore represents datainformation. At the receiver, the data can be decoded by checking thereceived OAM state. This approach seems to be more favorable to thequantum communications community, since OAM could provide for theencoding of multiple bits (log 2(N)) per photon due to the infinitelycountable possibilities of the OAM states, and so could potentiallyachieve a higher photon efficiency. The encoding/decoding of OAM statescould also have some potential applications for on-chip interconnectionto increase computing speed or data capacity.

The second approach is to use each OAM beam as a different data carrierin an SDM (Spatial Division Multiplexing) system. For an SDM system, onecould use either a multi-core fiber/free space laser beam array so thatthe data channels in each core/laser beam are spatially separated, oruse a group of orthogonal mode sets to carry different data channels ina multi-mode fiber (MMF) or in free space. Greater than 1 petabit/s datatransmission in a multi-core fiber and up to 6 linearly polarized (LP)modes each with two polarizations in a single core multi-mode fiber hasbeen reported. Similar to the SDM using orthogonal modes, OAM beams withdifferent states can be spatially multiplexed and demultiplexed, therebyproviding independent data carriers in addition to wavelength andpolarization. Ideally, the orthogonality of OAM beams can be maintainedin transmission, which allows all the data channels to be separated andrecovered at the receiver. A typical embodiments of OAM multiplexing isconceptually depicted in FIG. 11. An obvious benefit of OAM multiplexingis the improvement in system spectral efficiency, since the samebandwidth can be reused for additional data channels.

OAM Beam Generation and Detection

Many approaches for creating OAM beams have been proposed anddemonstrated. One could obtain a single or multiple OAM beams directlyfrom the output of a laser cavity, or by converting a fundamentalGaussian beam into an OAM beam outside a cavity. The converter could bea spiral phase plate, diffractive phase holograms, metalmaterials,cylindrical lens pairs, q-plates or fiber structures. There are alsodifferent ways to detect an OAM beam, such as using a converter thatcreates a conjugate helical phase, or using a plasmonic detector.

Mode Conversion Approaches

Referring now to FIG. 12, among all external-cavity methods, perhaps themost straightforward one is to pass a Gaussian beam through a coaxiallyplaced spiral phase plate (SPP) 1202. An SPP 1202 is an optical elementwith a helical surface, as shown in FIG. 12A. To produce an OAM beamwith a state of l, the thickness profile of the plate should be machinedas lλθ/2π(n−1), where n is the refractive index of the medium. Alimitation of using an SPP 1202 is that each OAM state requires adifferent specific plate. As an alternative, reconfigurable diffractiveoptical elements, e.g., a pixelated spatial light modulator (SLM) 1204,or a digital micro-mirror device can be programmed to function as anyrefractive element of choice at a given wavelength. As mentioned above,a helical phase profile exp(ilθ) converts a linearly polarized Gaussianlaser beam into an OAM mode, whose wave front resembles an f-foldcorkscrew 1206, as shown at 1204. Importantly, the generated OAM beamcan be easily changed by simply updating the hologram loaded on the SLM1204. To spatially separate the phase-modulated beam from thezeroth-order non-phase-modulated reflection from the SLM, a linear phaseramp is added to helical phase code (i.e., a “fork”-like phase pattern1208 to produce a spatially distinct first-order diffracted OAM beam,carrying the desired charge. It should also be noted that theaforementioned methods produce OAM beams with only an azimuthal indexcontrol. To generate a pure LG_(l,p) mode, one must jointly control boththe phase and the intensity of the wavefront. This could be achievedusing a phase-only SLM with a more complex phase hologram.

OAM Beams Multiplexing and Demultiplexing

One of the benefits of OAM is that multiple coaxially propagating OAMbeams with different l states provide additional data carriers as theycan be separated based only on the twisting wavefront. Hence, one of thecritical techniques is the efficient multiplexing/demultiplexing of OAMbeams of different t states, where each carries an independent datachannel and all beams can be transmitted and received using a singleaperture pair. Several multiplexing and demultiplexing techniques havebeen demonstrated, including the use of an inverse helical phasehologram to down-convert the OAM into a Gaussian beam, a mode sorter,free-space interferometers, a photonic integrated circuit, and q-plates.Some of these techniques are briefly described below.

Beam Splitter and Inverse Phase Hologram

A straightforward way of multiplexing is simply to use cascaded 3-dBbeam splitters (BS) 1302. Each BS 1302 can coaxially multiplex two beams1303 that are properly aligned, and cascaded N BSs can multiplex N+1independent OAM beams at most, as shown in FIG. 13A. Similarly, at thereceiver end, the multiplexed beam 1305 is divided into four copies 1304by BS 1302. To demultiplex the data channel on one of the beams (e.g.,with l=1_i), a phase hologram 1306 with a spiral charge of

−1

_i is applied to all the multiplexed beams 1304. As a result, thehelical phase on the target beam is removed, and this beam evolves intoa fundamental Gaussian beam, as shown in FIG. 13B. The down-convertedbeam can be isolated from the other beams, which still have helicalphase fronts by using a spatial mode filter 1308 (e.g., a single modefiber only couples the power of the fundamental Gaussian mode due to themode matching theory). Accordingly, each of the multiplexed beams 1304can be demultiplexed by changing the spiral phase hologram 1306.Although this method is very power-inefficient since the BSs 1302 andthe spatial mode filter 1306 cause a lot of power loss, it was used inthe initial lab demonstrations of OAM multiplexing/demultiplexing, dueto the simplicity of understanding and the reconfigurability provided byprogrammable SLMs.

Optical Geometrical Transformation-Based Mode Sorter

Referring now to FIG. 14, another method of multiplexing anddemultiplexing, which could be more power-efficient than the previousone (using beam splitters), is the use of an OAM mode sorter. This modesorter usually comprises three optical elements, including a transformer1402, a corrector 1404, and a lens 1406, as shown in FIG. 14. Thetransformer 1402 performs a geometrical transformation of the input beamfrom log-polar coordinates to Cartesian coordinates, such that theposition (x,y) in the input plane is mapped to a new position (u,v) inthe output plane, where

${u = {{- a}\; {\ln( \frac{\sqrt{x^{2} + y^{2}}}{b} )}}},$

and v=a arctan(y/x). Here, a and b are scaling constants. The corrector1404 compensates for phase errors and ensures that the transformed beamis collimated. Considering an input OAM beam with a ring-shaped beamprofile, it can be unfolded and mapped into a rectangular-shaped planewave with a tilted phase front. Similarly, multiple OAM beams havingdifferent 1 states will be transformed into a series of plane waves eachwith a different phase tilt. A lens 1406 focuses these tilted planewaves into spatially separated spots in the focal plane such that allthe OAM beams are simultaneously demultiplexed. As the transformation isreciprocal, if the mode sorter is used in reverse it can become amultiplexer for OAM. A Gaussian beam array placed in the focal plane ofthe lens 1406 is converted into superimposed plane waves with differenttilts. These beams then pass through the corrector and the transformersequentially to produce properly multiplexed OAM beams.

Free Space Communications

The first proof-of-concept experiment using OAM for free spacecommunications transmitted eight different OAM states each representinga data symbol one at a time. The azimuthal index of the transmitted OAMbeam is measured at the receiver using a phase hologram modulated with abinary grating. To effectively use this approach, fast switching isrequired between different OAM states to achieve a high data rate.Alternatively, classic communications using OAM states as data carrierscan be multiplexed at the transmitter, co-propagated through a freespace link, and demultiplexed at a receiver. The total data rate of afree space communication link has reached 100 Tbit/s or even beyond byusing OAM multiplexing. The propagation of OAM beams through a realenvironment (e.g., across a city) is also under investigation.

Basic Link Demonstrations

Referring now to FIGS. 15A-15C, initial demonstrates of using OAMmultiplexing for optical communications include free space links using aGaussian beam and an OAM beam encoded with OOK data. Four monochromaticGaussian beams each carrying an independent 50.8 Gbit/s (4×12.7 Gbit/s)16-QAM signal were prepared from an IQ modulator and free-spacecollimators. The beams were converted to OAM beams with l=−8, +10, +12and −14, respectively, using 4 SLMs each loaded with a helical phasehologram, as shown in FIG. 15A. After being coaxially multiplexed usingcascaded 3 dB-beam splitters, the beams were propagated through ˜1 mdistance in free-space under lab conditions. The OAM beams were detectedone at a time, using an inverse helical phase hologram and a fibercollimator together with a SMF. The 16-QAM data on each channel wassuccessfully recovered, and a spectral efficiency of 12.8 bit/s/Hz inthis data link was achieved, as shown in FIGS. 15B and 15C.

A following experiment doubled the spectral efficiency by adding thepolarization multiplexing into the OAM-multiplexed free-space data link.Four different OAM beams (l=+4, +8, −8, +16) on each of two orthogonalpolarizations (eight channels in total) were used to achieve a Terabit/stransmission link. The eight OAM beams were multiplexed anddemultiplexed using the same approach as mentioned above. The measuredcrosstalk among channels carried by the eight OAM beams is shown inTable 1, with the largest crosstalk being ˜−18.5 dB. Each of the beamswas encoded with a 42.8 Gbaud 16-QAM signal, allowing a total capacityof ˜1.4 (42.8×4×4×2) Tbit/s.

TABLE 1 OAM₊₄ OAM₊₈ OAM⁻⁸ OAM₊₁₆ Measured Crosstalk X-Pol. Y-Pol. X-Pol.Y-Pol. X-Pol. Y-Pol. X-Pol Y-Pol. OAM₊₄(dB) X-Pol. −23.2 −26.7 −30.8−30.5 −27.7 −24.6 −30.1 Y-Pol. −25.7 OAM₊₈(dB) X-Pol. −26.6 −23.5 −21.6−18.8 −25.4 −23.8 −28.8 Y-Pol. −25.0 OAM⁻⁸(dB) X-Pol. −27.5 −33.9 −27.6−30.8 −20.5 −26.5 −21.8 Y-Pol. −26.8 OAM₊₁₆(dB) X-Pol. −24.5 −31.2 −23.7−23.3 −25.8 −26.1 −30.2 Y-Pol. −24.0 Total from other OAMs *(dB) −21.8−21.0 −21.2 −21.4 −18.6 −21.2 −22.2 −20.7

The capacity of the free-space data link was further increased to 100Tbit/s by combining OAM multiplexing with PDM (phase divisionmultiplexing) and WDM (wave division multiplexing). In this experiment,24 OAM beams (l=±4, ±7, ±10, ±13, ±16, and ±19, each with twopolarizations) were prepared using 2 SLMs, the procedures for which areshown in FIG. 16 at 1602-1606. Specifically, one SLM generated asuperposition of OAM beams with l=+4, +10, and +16, while the other SLMgenerated another set of three OAM beams with l=+7, +13, and +19 (FIG.16A). These two outputs were multiplexed together using a beam splitter,thereby multiplexing six OAM beams: l=+4, +7, +10, +13, +16, and +19(FIG. 16A). Secondly, the six multiplexed OAM beams were split into twocopies. One copy was reflected five times by three mirrors and two beamsplitters, to create another six OAM beams with inverse charges (FIG.16B). There was a differential delay between the two light paths tode-correlate the data. These two copies were then combined again toachieve 12 multiplexed OAM beams with l=±4, ±7, ±10, ±13, ±16, and ±19(FIG. 16B). These 12 OAM beams were split again via a beam splitter. Oneof these was polarization-rotated by 90 degrees, delayed by ˜33 symbols,and then recombined with the other copy using a polarization beamsplitter (PBS), finally multiplexing 24 OAM beams (with l=±4, ±7, ±10,±13, ±16, and ±19 on two polarizations). Each of the beam carried a WDMsignal comprising 100 GHz-spaced 42 wavelengths (1,536.34-1,568.5 nm),each of which was modulated with 100 Gbit/s QPSK data. The observedoptical spectrum of the WDM signal carried on one of the demultiplexedOAM beams (l=+10).

Atmospheric Turbulence Effects on OAM Beams

One of the critical challenges for a practical free-space opticalcommunication system using OAM multiplexing is atmospheric turbulence.It is known that inhomogeneities in the temperature and pressure of theatmosphere lead to random variations in the refractive index along thetransmission path, and can easily distort the phase front of a lightbeam. This could be particularly important for OAM communications, sincethe separation of multiplexed OAM beams relies on the helicalphase-front. As predicted by simulations in the literature, theserefractive index inhomogeneities may cause inter-modal crosstalk amongdata channels with different OAM states.

The effect of atmospheric turbulence is also experimentally evaluated.For the convenience of estimating the turbulence strength, one approachis to emulate the turbulence in the lab using an SLM or a rotating phaseplate. FIG. 17A illustrates an emulator built using a thin phase screenplate 1702 that is mounted on a rotation stage 1704 and placed in themiddle of the optical path. The pseudo-random phase distributionmachined on the plate 1702 obeys Kolmogorov spectrum statistics, whichare usually characterized by a specific effective Fried coherence lengthr0. The strength of the simulated turbulence 1706 can be varied eitherby changing to a plate 1702 with a different r0, or by adjusting thesize of the beam that is incident on the plate. The resultant turbulenceeffect is mainly evaluated by measuring the power of the distorted beamdistributed to each OAM mode using an OAM mode sorter. It was foundthat, as the turbulence strength increases, the power of the transmittedOAM mode would leak to neighboring modes and tend to be equallydistributed among modes for stronger turbulence. As an example, FIG. 17Bshows the measured average power (normalized) l=3 beam under differentemulated turbulence conditions. It can be seen that the majority of thepower is still in the transmitted OAM mode 1708 under weak turbulence,but it spreads to neighboring modes as the turbulence strengthincreases.

Turbulence Effects Mitigation Techniques

One approach to mitigate the effects of atmospheric turbulence on OAMbeams is to use an adaptive optical (AO) system. The general idea of anAO system is to measure the phase front of the distorted beam first,based on which an error correction pattern can be produced and can beapplied onto the beam transmitter to undo the distortion. As for OAMbeams with helical phase fronts, it is challenging to directly measurethe phase front using typical wavefront sensors due to the phasesingularity. A modified AO system can overcome this problem by sending aGaussian beam as a probe beam to sense the distortion, as shown in FIG.18A. Due to the fact that turbulence is almost independent of the lightpolarization, the probe beam is orthogonally polarized as compared toall other beams for the sake of convenient separation at beam separator1802. The correction phase pattern can be derived based on the probebeam distortion that is directly measured by a wavefront sensor 1704. Itis noted that this phase correction pattern can be used tosimultaneously compensate multiple coaxially propagating OAM beams. FIG.18 at 1810-1820 illustrate the intensity profiles of OAM beams with l=1,5 and 9, respectively, for a random turbulence realization with andwithout mitigation. From the far-field images, one can see that thedistorted OAM beams (upper), up to l=9, were partially corrected, andthe measured power distribution also indicates that the channelcrosstalk can be reduced.

Another approach for combating turbulence effects is to partially movethe complexity of optical setup into the electrical domain, and usedigital signal processing (DSP) to mitigate the channel crosstalk. Atypical DSP method is the multiple-input-multiple-output (MIMO)equalization, which is able to blindly estimate the channel crosstalkand cancel the interference. The implementation of a 4×4 adaptive MIMOequalizer in a four-channel OAM multiplexed free space optical linkusing heterodyne detection may be used. Four OAM beams (l=+2, +4, +6 and+8), each carrying 20 Gbit/s QPSK data, were collinearly multiplexed andpropagated through a weak turbulence emulated by the rotating phaseplate under laboratory condition to introduce distortions. Afterdemultiplexing, four channels were coherently detected and recordedsimultaneously. The standard constant modulus algorithm is employed inaddition to the standard procedures of coherent detection to equalizethe channel interference. Results indicate that MIMO equalization couldbe helpful to mitigate the crosstalk caused by either turbulence orimperfect mode generation/detection, and improve both error vectormagnitude (EVM) and the bit-error-rate (BER) of the signal in anOAM-multiplexed communication link.

MIMO DSP may not be universally useful as outage could happen in somescenarios involving free space data links. For example, the majoritypower of the transmitted OAM beams may be transferred to other OAMstates under a strong turbulence without being detected, in which caseMIMO would not help to improve the system performance.

OAM Free Space Link Design Considerations

To date, most of the experimental demonstrations of opticalcommunication links using OAM beams took place in the lab conditions.There is a possibility that OAM beams may also be used in a free spaceoptical communication link with longer distances. To design such a datalink using OAM multiplexing, several important issues such as beamdivergence, aperture size and misalignment of two transmitter andreceiver, need to be resolved. To study how those parameters affect theperformance of an OAM multiplexed system, a simulation model wasdescribed by Xie et al, the schematic setup of which is shown in FIG.19. Each of the different collimated Gaussian beams 1902 at the samewavelength is followed by a spiral phase plate 1904 with a unique orderto convert the Gaussian beam into a data-carrying OAM beam. Differentorders of OAM beams are then multiplexed at multiplexor 1906 to form aconcentric-ring-shape and coaxially propagate from transmitter 1908through free space to the receiver aperture located at a certainpropagation distance. Propagation of multiplexed OAM beams isnumerically propagated using the Kirchhoff-Fresnel diffraction integral.To investigate the signal power and crosstalk effect on neighboring OAMchannels, power distribution among different OAM modes is analyzedthrough a modal decomposition approach, which corresponds to the casewhere the received OAM beams are demultiplexed without power loss andthe power of a desired OAM channel is completely collected by itsreceiver 1910.

Beam Divergence

For a communication link, it is generally preferable to collect as muchsignal power as possible at the receiver to ensure a reasonablesignal-to-noise ratio (SNR). Based on the diffraction theory, it isknown that a collimated OAM beam diverges while propagating in freespace. Given the same spot size of three cm at the transmitter, an OAMbeam with a higher azimuthal index diverges even faster, as shown inFIG. 20A. On the other hand, the receiving optical element usually has alimited aperture size and may not be able to collect all of the beampower. The calculated link power loss as a function of receiver aperturesize is shown in FIG. 35B, with different transmission distances andvarious transmitted beam sizes. Unsurprisingly, the power loss of a 1-kmlink is higher than that of a 100-m link under the same transmitted beamsize due to larger beam divergence. It is interesting to note that asystem with a transmitted beam size of 3 cm suffers less power loss thanthat of 1 cm and 10 cm over a 100-m link. The 1-cm transmitted beamdiverges faster than the 3 cm beam due to its larger diffraction.However, when the transmitted beam size is 10 cm, the geometricalcharacteristics of the beam dominate over the diffraction, thus leadinglarger spot size at the receiver than the 3 cm transmitted beam. Atrade-off between the diffraction, geometrical characteristics and thenumber of OAMs of the beam therefore needs to be carefully considered inorder to achieve a proper-size received beam when designing a link.

Misalignment Tolerance

Referring now to FIGS. 21A-21C, besides the power loss due tolimited-size aperture and beam divergence, another issue that needsfurther discussion is the potential misalignment between the transmitterand the receiver. In an ideal OAM multiplexed communication link,transmitter and receiver would be perfectly aligned, (i.e., the centerof the receiver would overlap with the center of the transmitted beam2102, and the receiver plane 2104 would be perpendicular to the lineconnecting their centers, as shown in FIG. 21A). However, due todifficulties in aligning because of substrate distances, and jitter andvibration of the transmitter/receiver platform, the transmitter andreceiver may have relative lateral shift (i.e., lateral displacement)(FIG. 21B) or angular shift (i.e., receiver angular error) (FIG. 21C).Both types of misalignment may lead to degradation of systemperformance.

Focusing on a link distance of 100 m, FIGS. 22A and 22B show the powerdistribution among different OAM modes due to lateral displacement andreceiver angular error when only l=+3 is transmitted with a transmittedbeam size of 3 cm. In order to investigate the effect of misalignment,the receiver aperture size is chosen to be 10 cm, which could cover thewhole OAM beam at the receiver. As the lateral displacement or receiverangular error increases, power leakage to other modes (i.e., channelcrosstalk) increases while the power on l=+3 state decreases. This isbecause larger lateral displacement or receiver angular causes largerphase profile mismatch between the received OAM beams and receiver. Thepower leakage to l=+1 and l=+5 is greater than that of l=+2 and l=+3 dueto their larger mode spacing with respect to l=+3. Therefore, a systemwith larger mode spacing (which also uses higher order OAM statessuffers less crosstalk. However, such a system may also have a largerpower loss due to the fast divergence of higher order OAM beams, asdiscussed above. Clearly, this trade-off between channel crosstalk andpower loss shall be considered when choosing the mode spacing in aspecific OAM multiplexed link.

An additional configuration in which the optical angular momentumprocessing and multi-layer overlay modulation technique described hereinabove may prove useful within the optical network framework is use withfree-space optics communications. Free-space optics systems provide anumber of advantages over traditional RF based systems from improvedisolation between the systems, the size and the cost of thereceivers/transmitters, need for an FCC license, and by combining space,lighting, and communication into the same system. Referring now to FIG.23, there is illustrated an example of the operation of a free-spacecommunication system. The free-space communication system utilizes afree-space optics transmitter 2302 that transmits a light beam 2304 to afree-space optics receiver 2306. The major difference between afiber-optic network and a free-space optic network is that theinformation beam is transmitted through free space rather than over afiber-optic cable. This causes a number of link difficulties, which willbe more fully discussed herein below. However, because the free spacesystem does not have the optic fiber to act as a waveguide, it is moresusceptible to the problems outlined above. Free-space optics is a lineof sight technology that uses the invisible beams of light to provideoptical bandwidth connections that can send and receive up to 2.5 Gbpsof data, voice, and video communications between a transmitter 2302 anda receiver 2306. Free-space optics uses the same concepts asfiber-optics, except without the use of a fiber-optic cable. Free-spaceoptics systems provide the light beam 2304 within the infrared (IR)spectrum, which is at the low end of the light spectrum. Specifically,the optical signal is in the range of 300 Gigahertz to 1 Terahertz interms of wavelength.

Presently existing free-space optics systems can provide data rates ofup to 10 Gigabits per second at a distance of up to 2.5 kilometers. Inouter space, the communications range of free space opticalcommunications is currently on the order of several thousand kilometers,but has the potential to bridge interplanetary distances of millions ofkilometers, using optical telescopes as beam expanders. In January of2013, NASA used lasers to beam an image of the Mona Lisa to the LunarReconnaissance Orbiter roughly 240,000 miles away. To compensate foratmospheric interference, an error correction code algorithm, similar tothat used within compact discs, was implemented.

Referring now to FIG. 24, there is illustrated a block diagram of afree-space optics system using orbital angular momentum and multileveloverlay modulation according to the present disclosure. The OAM twistedsignals, in addition to being transmitted over fiber, may also betransmitted using free optics. In this case, the transmission signalsare generated within transmission circuitry 2402 at each of the FSOtransceivers 2404. Free-space optics technology is based on theconnectivity between the FSO based optical wireless units, eachconsisting of an optical transceiver 2404 with a transmitter 2402 and areceiver 2406 to provide full duplex open pair and bidirectional closedpairing capability. Each optical wireless transceiver unit 2404additionally includes an optical source 2408 plus a lens or telescope2410 for transmitting light through the atmosphere to another lens 2410receiving the information. At this point, the receiving lens ortelescope 2410 connects to a high sensitivity receiver 2406 via opticalfiber 2412. The transmitting transceiver 2404 a and the receivingtransceiver 2404 b have to have line of sight to each other and bealigned both laterally and angularly. Obstacles, such as, trees,buildings, animals, and atmospheric conditions, all can hinder the lineof sight needed for this communications medium. Since line of sight isso critical, some systems make use of beam divergence or a diffused beamapproach, which involves a large field of view that toleratessubstantial line of sight interference without significant impact onoverall signal quality. The system may also be equipped with autotracking mechanism 2414 that maintains a tightly focused beam on thereceiving transceiver 1904 b, even when the transceivers are mounted ontall buildings or other structures that sway.

The modulated light source used with optical source 2408 is typically alaser or light emitting diode (LED) providing the transmitted opticalsignal that determines all the transmitter capabilities of the system.Only the detector sensitivity within the receiver 2406 plays an equallyimportant role in total system performance. For telecommunicationspurposes, only lasers that are capable of being modulated at 20 Megabitsper second to 2.5 Gigabits per second can meet current marketplacedemands. Additionally, how the device is modulated and how muchmodulated power is produced are both important to the selection of thedevice. Lasers in the 780-850 nm and 1520-1600 nm spectral bands meetfrequency requirements.

Commercially available FSO systems operate in the near IR wavelengthrange between 750 and 1600 nm, with one or two systems being developedto operate at the IR wavelength of 10,000 nm. The physics andtransmissions properties of optical energy as it travels through theatmosphere are similar throughout the visible and near IR wavelengthrange, but several factors that influence which wavelengths are chosenfor a particular system.

The atmosphere is considered to be highly transparent in the visible andnear IR wavelength. However, certain wavelengths or wavelength bands canexperience severe absorption. In the near IR wavelength, absorptionoccurs primarily in response to water particles (i.e., moisture) whichare an inherent part of the atmosphere, even under clear weatherconditions. There are several transmission windows that are nearlytransparent (i.e., have an attenuation of less than 0.2 dB perkilometer) within the 700-10,000 nm wavelength range. These wavelengthsare located around specific center wavelengths, with the majority offree-space optics systems designed to operate in the windows of 780-850nm and 1520-1600 nm.

Wavelengths in the 780-850 nm range are suitable for free-space opticsoperation and higher power laser sources may operate in this range. At780 nm, inexpensive CD lasers may be used, but the average lifespan ofthese lasers can be an issue. These issues may be addressed by runningthe lasers at a fraction of their maximum rated output power which willgreatly increase their lifespan. At around 850 nm, the optical source2408 may comprise an inexpensive, high performance transmitter anddetector components that are readily available and commonly used innetwork transmission equipment. Highly sensitive silicon (SI) avalanchephotodiodes (APD) detector technology and advanced vertical cavityemitting laser may be utilized within the optical source 2408.

VCSEL technology may be used for operation in the 780 to 850 nm range.Possible disadvantage of this technology include beam detection throughthe use of a night vision scope, although it is still not possible todemodulate a perceived light beam using this technique.

Wavelengths in the 1520-1600 nm range are well-suited for free-spacetransmission, and high quality transmitter and detector components arereadily available for use within the optical source block 2408. Thecombination of low attenuation and high component availability withinthis wavelength range makes the development of wavelength divisionmultiplexing (WDM) free-space optics systems feasible. However,components are generally more expensive and detectors are typically lesssensitive and have a smaller receive surface area when compared withsilicon avalanche photodiode detectors that operator at the 850 nmwavelength. These wavelengths are compatible with erbium-doped fiberamplifier technology, which is important for high power (greater than500 milliwatt) and high data rate (greater than 2.5 Gigabytes persecond) systems. Fifty to 65 times as much power can be transmitted atthe 1520-1600 nm wavelength than can be transmitted at the 780-850 nmwavelength for the same eye safety classification. Disadvantages ofthese wavelengths include the inability to detect a beam with a nightvision scope. The night vision scope is one technique that may be usedfor aligning the beam through the alignment circuitry 2414. Class 1lasers are safe under reasonably foreseeable operating conditionsincluding the use of optical instruments for intrabeam viewing. Class 1systems can be installed at any location without restriction.

Another potential optical source 2408 comprised Class 1M lasers. Class1M laser systems operate in the wavelength range from 302.5 to 4000 nm,which is safe under reasonably foreseeable conditions, but may behazardous if the user employs optical instruments within some portion ofthe beam path. As a result, Class 1M systems should only be installed inlocations where the unsafe use of optical aids can be prevented.Examples of various characteristics of both Class 1 and Class 1M lasersthat may be used for the optical source 2408 are illustrated in Table 2below.

TABLE 2 Laser Power Aperture Size Distance Power Density Classification(mW) (mm) (m) (mW/cm²) 850-nm Wavelength Class 1 0.78 7 14 2.03 50 20000.04 Class 1M 0.78 7 100 2.03 500 7 14 1299.88 50 2000 25.48 1550-nmWavelength Class 1 10 7 14 26.00 25 2000 2.04 Class 1M 10 3.5 100 103.99500 7 14 1299.88 25 2000 101.91

The 10,000 nm wavelength is relatively new to the commercial free spaceoptic arena and is being developed because of better fog transmissioncapabilities. There is presently considerable debate regarding thesecharacteristics because they are heavily dependent upon fog type andduration. Few components are available at the 10,000 nm wavelength, asit is normally not used within telecommunications equipment.Additionally, 10,000 nm energy does not penetrate glass, so it isill-suited to behind window deployment.

Within these wavelength windows, FSO systems should have the followingcharacteristics. The system should have the ability to operate at higherpower levels, which is important for longer distance FSO systemtransmissions. The system should have the ability to provide high speedmodulation, which is important for high speed FSO systems. The systemshould provide a small footprint and low power consumption, which isimportant for overall system design and maintenance. The system shouldhave the ability to operate over a wide temperature range without majorperformance degradations such that the systems may prove useful foroutdoor systems. Additionally, the mean time between failures shouldexceed 10 years. Presently existing FSO systems generally use VCSELS foroperation in the shorter IR wavelength range, and Fabry-Pérot ordistributed feedback lasers for operation in the longer IR wavelengthrange. Several other laser types are suitable for high performance FSOsystems.

A free-space optics system using orbital angular momentum processing andmulti-layer overlay modulation would provide a number of advantages. Thesystem would be very convenient. Free-space optics provides a wirelesssolution to a last-mile connection, or a connection between twobuildings. There is no necessity to dig or bury fiber cable. Free-spaceoptics also requires no RF license. The system is upgradable and itsopen interfaces support equipment from a variety of vendors. The systemcan be deployed behind windows, eliminating the need for costly rooftopsites. Further, it is easier to deploy in buildings as the system can belocated as the area requires, saving significant costs of running cablesto rooftops. It is also immune to radiofrequency interference orsaturation. The system is also fairly speedy. The system provides 10Gigabits per second of data throughput. This provides ample bandwidth totransfer files between two sites. With the growth in the size of files,free-space optics provides the necessary bandwidth to transfer thesefiles efficiently.

Free-space optics also provides a secure wireless solution. The laserbeam cannot be detected with a spectral analyzer or RF meter. The beamis invisible, which makes it difficult to find. The laser beam that isused to transmit and receive the data is very narrow. This means that itis almost impossible to intercept the data being transmitted. One wouldhave to be within the line of sight between the receiver and thetransmitter in order to be able to accomplish this feat. If this occurs,this would alert the receiving site that a connection has been lost orthe amount of signal received severely diminished. Thus, minimalsecurity upgrades would be required for a free-space optics system.

However, there are several weaknesses with free-space optics systems.The distance of a free-space optics system is very limited. Currentlyoperating distances are approximately within 2 kilometers. Although thisis a powerful system with great throughput, the limitation of distanceis a big deterrent for full-scale implementation. Further, the more OAMsapplied, the greater divergence over distance. Additionally, all systemsrequire line of sight be maintained at all times during transmission.Any obstacle, be it environmental or animals can hinder thetransmission. Free-space optic technology must be designed to combatchanges in the atmosphere which can affect free-space optic systemperformance capacity. Finally, any shift in the mounting apparatus cancause the beam to be misaligned. Shifts can be caused by wind,earthquakes, ground shifting and even traffic.

Referring now to FIGS. 25A through 25D, in order to achieve higher datacapacity within optical links, an additional degree of freedom frommultiplexing multiple data channels must be exploited. Moreover, theability to use two different orthogonal multiplexing techniques togetherhas the potential to dramatically enhance system performance andincreased bandwidth.

One multiplexing technique which may exploit the possibilities is modedivision multiplexing (MDM) using orbital angular momentum (OAM). OAMmode refers to laser beams within a free-space optical system orfiber-optic system that have a phase term of e^(ilφ) in their wavefronts, in which φ is the azimuth angle and l determines the OAM value(topological charge). In general, OAM modes have a “donut-like” ringshaped intensity distribution. Multiple spatial collocated laser beams,which carry different OAM values, are orthogonal to each other and canbe used to transmit multiple independent data channels on the samewavelength. Consequently, the system capacity and spectral efficiency interms of bits/S/Hz can be dramatically increased. Free-spacecommunications links using OAM may support 100 Tbits/capacity. Varioustechniques for implementing this as illustrated in FIGS. 25A through 25Dinclude a combination of multiple beams 2502 having multiple differentOAM values 2504 on each wavelength. Thus, beam 2502 includes OAM values,OAM1 and OAM4. Beam 2506 includes OAM value 2 and OAM value 5. Finally,beam 2508 includes OAM3 value and OAM6 value. Referring now to FIG. 25B,there is illustrated a single beam wavelength 2510 using a first groupof OAM values 2512 having both a positive OAM value 2512 and a negativeOAM value 2514. Similarly, OAM2 value may have a positive value 2516 anda negative value 2518 on the same wavelength 2510. While mode divisionmultiplexing of OAM modes is described above, other orthogonal functionsmay be used with mode division multiplexing such as Laguerre Gaussianfunctions, Hermite Gaussian functions, Jacobi functions, Gegenbauerfunctions, Legendre functions and Chebyshev functions.

FIG. 25C illustrates the use of a wavelength 2520 having polarizationmultiplexing of OAM value. The wavelength 2520 can have multiple OAMvalues 2522 multiplexed thereon. The number of available channels can befurther increased by applying left or right handed polarization to theOAM values. Finally, FIG. 25D illustrates two groups of concentric rings2560, 2562 for a wavelength having multiple OAM values.

Another multiplexing technique is wavelength distribution multiplexing(WDM), WDM has been widely used to improve the optical communicationcapacity within both fiber-optic systems and free-space communicationsystem. Combining OAM and WDM has not previously been done. However, OAMmode multiplexing and WDM are mutually orthogonal such that they can becombined to achieve a dramatic increase in system capacity. Referringnow to FIG. 26, there is illustrated a scenario where each WDM channel2602 contains many orthogonal OAM beam 2604. Thus, using a combinationof orbital angular momentum with wave division multiplexing, asignificant enhancement in communication link to capacity may beachieved.

Current optical communication architectures have considerable routingchallenges. A routing protocol for use with free-space optic system musttake into account the line of sight requirements for opticalcommunications within a free-space optics system. However, an opticsnetwork may be modeled as a directed hierarchical random sectorgeometric graph in which sensors route their data via multi-hop paths toa base station through a cluster head. This technique is a new efficientrouting algorithm for local neighborhood discovery and a base stationuplink and downlink discovery algorithm. The routing protocol requiresorder Olog(n) storage at each node versus order O(n) used within currenttechniques and architectures. This new technique has the advantage ofbeing much faster than current systems.

Current routing protocols are based on link state, distance vectors,path vectors, or source routing, and they differ from the new routingtechnique in significant manners. First, current techniques assume thata fraction of the links are bidirectional. This is not true within afree-space optic network in which links are unidirectional. Second, manycurrent protocols are designed for ad hoc networks in which the routingprotocol is designed to support multi-hop communications between anypair of nodes. The goal of the sensor network is to route sensorreadings to the base station. Therefore, the dominant traffic patternsare different from those in an ad hoc network. In a sensor network, nodeto base stations, base station to nodes, and local neighborhoodcommunication are mostly used.

Many paths of wireless and free space network are unidirectional. Recentstudies on wireless and free space optical systems show that as many as5 percent to 10 percent of links and wireless ad hoc networks areunidirectional due to various factors. Routing protocols such as DSDVand AODV use a reverse path technique, implicitly ignoring suchunidirectional links and are therefore not relevant in this scenario.Other protocols such as DSR, ZRP, or ZRL have been designed or modifiedto accommodate unidirectionality by detecting unidirectional links andthen providing bidirectional abstraction for such links.Unidirectionality only allows information transmission in a singledirection which does not enable a response to be provided to aninformation transmission system. Referring now to FIG. 27, one solutionfor dealing with unidirectionality is tunneling, in whichbidirectionality is emulated for a unidirectional link by usingbidirectional links on a reverse back channel to establish the tunnel.Tunneling also prevents implosion of acknowledgement packets and loopingby simply pressing link layer acknowledgements for tunneled packetsreceived on a unidirectional link. Tunneling, however, works well inmostly bidirectional networks with few unidirectional links.

Within a network using only unidirectional links such as a free-spaceoptical network, systems such as that illustrated in FIGS. 27 and 28would be more applicable. Nodes within a unidirectional network utilizea directional transmit 2702 transmitting from the node 2700 in a single,defined direction. Additionally, each node 2700 includes anomnidirectional receiver 2704 which can receive a signal coming to thenode in any direction. Also, as discussed here and above, the node 2700would also include a θlog(n) storage 2706. Thus, each node 2700 provideonly unidirectional communications links. Thus, a series of nodes 2700as illustrated in FIG. 28 may unidirectionally communicate with anyother node 2700 and forward communication from one location to anotherthrough a sequence of interconnected nodes.

Multiplexing of the topological charge to the RF as well as free spaceoptics in real time provides redundancy and better capacity. Whenchannel impairments from atmospheric disturbances or scintillationimpact the information signals, it is possible to toggle between freespace optics to RF and back in real time. This approach still usestwisted waves on both the free space optics as well as the RF signal.Most of the channel impairments can be detected using a control or pilotchannel and be corrected using algorithmic techniques (closed loopcontrol system) or by toggling between the RF and free space optics.

Topological charge may be multiplexed to the wave length for eitherlinear or circular polarization. In the case of linear polarizations,topological charge would be multiplexed on vertical and horizontalpolarization. In case of circular polarization, topological charge wouldbe multiplexed on left hand and right hand circular polarizations.

The topological charges can be created using Spiral Phase Plates (SPPs)such as that illustrated in FIG. 11E, phase mask holograms or a SpatialLight Modulator (SLM) by adjusting the voltages on SLM which createsproperly varying index of refraction resulting in twisting of the beamwith a specific topological charge. Different topological charges can becreated and muxed together and de-muxed to separate charges.

As Spiral Phase plates can transform a plane wave (l=0) to a twistedwave of a specific helicity (i.e. l=+1), Quarter Wave Plates (QWP) cantransform a linear polarization (s=0) to circular polarization (i.e.s=+1).

Cross talk and multipath interference can be reduced usingMultiple-Input-Multiple-Output (MIMO).

Most of the channel impairments can be detected using a control or pilotchannel and be corrected using algorithmic techniques (closed loopcontrol system).

In a further embodiment illustrated in FIG. 29, both RF signals and freespace optics may be implemented within a dual RF and free space opticsmechanism 2902. The dual RF and free space optics mechanism 2902 includea free space optics projection portion 2904 that transmits a light wavehaving an orbital angular momentum applied thereto with multileveloverlay modulation and a RF portion 2906 including circuitry necessaryfor transmitting information with orbital angular momentum andmultilayer overlay on an RF signal 2910. The dual RF and free spaceoptics mechanism 2902 may be multiplexed in real time between the freespace optics signal 2908 and the RF signal 2910 depending upon operatingconditions. In some situations, the free space optics signal 2908 wouldbe most appropriate for transmitting the data. In other situations, thefree space optics signal 2908 would not be available and the RF signal2910 would be most appropriate for transmitting data. The dual RF andfree space optics mechanism 2902 may multiplex in real time betweenthese two signals based upon the available operating conditions.

Multiplexing of the topological charge to the RF as well as free spaceoptics in real time provides redundancy and better capacity. Whenchannel impairments from atmospheric disturbances or scintillationimpact the information signals, it is possible to toggle between freespace optics to RF and back in real time. This approach still usestwisted waves on both the free space optics as well as the RF signal.Most of the channel impairments can be detected using a control or pilotchannel and be corrected using algorithmic techniques (closed loopcontrol system) or by toggling between the RF and free space optics.

Referring now to FIG. 30, there is illustrated a further manner forgenerating a light beam 3002 including orthogonal functions such as OAM,Hermite Gaussian, Laguerre Gaussian, etc., therein to encode informationin the beam. The laser beam generator 3004 generates a beam 3006including plane waves that is provided to a MicroElectroMechanicalsystem (MEMs) device 3008. Examples of MEMs devices 3008 include digitallight processing (DLP) projectors or digital micro-mirror devices (DMDs)that enable the generation of light beams having variouscharacteristics. A MEMs device 3008 can generate Hermite Gaussian (HG)modes, Laguerre Gaussian (LG) modes and vortex OAM modes that areprogrammed responsive to inputs to the MEMs device 3008. The MEMs device3008 has mode selection logic 3010 that enable selection of the LaguerreGaussian, Hermite Gaussian and vortex OAM modes (or other orthogonalfunction modes) for processing of the incoming light beam 3006. The MEMsdevice 3008 further enables switching between the different modes at avery high rate of a few thousand times per second which is notachievable using spatial light modulator (SLMs). Switching between themodes is controlled via mode switching logic 3012. This fast switchingenables these forms of OAM, HG or LG mode generation for communicationsas well as quantum key distribution (QKD) and quantum computers forquantum information processing. The orthogonal characteristics ofLaguerre-Gaussian (LG) with OAM and Hermite-Gaussian (HG) beams combinedwith high-speed switching of MEMs make the device useful in achievinghigher data capacity. This is possible using holograms that areprogrammed into the memory of a DLP that program micro-mirrors toselected positions and can twist a light beam with programmedinformation using the mirrors.

This enables the on-demand realization of binary gratings (holograms)that can be switched between at very high speed using an externaldigital signal. Using, for example, DLP technologies, a switch betweendifferent modes (different binary gratings) may be achieved at a veryhigh rate of speed of a few thousand times per second which is notachievable using spatial light modulators (SLMs). This allows for thedynamic control of helicities provided to a beam of light for a newmodulation and/or multiple access technique to encode information.

DLP's allow for high resolution and accuracy from micrometers tomillimeters thus enabling a variety of frequencies from infrared toultraviolet to be utilized. The use of DLP's for MDM (mode divisionmultiplexing) minimizes color, distance, movement and environmentalsensitivity and is thus ideal for building integrated optics. Themajority of SLM's are limited by a frame refresh rate of about 60 Hzwhich makes the high speed, wide range of operational spectral bandwidthof digital micro-mirror devices (DMD's) useful in a variety ofapplications. DMD designs inherently minimize temperature sensitivityfor reliable 3-D wave construction.

The vast majority of commercially available SLM devices are limited toframe rate of about 60 Hz which considerably limits the speed ofoperation of any system based on this technology. A DMD is an amplitudeonly spatial light modulator. The high speed, wide range of operationalspectral bandwidth and high power threshold of a DMDs makes the device auseful tool for variety of applications. Variations of DMD's arecommercially available for a fraction of the cost of a phase only SLM.Intensity shaping of spatial modes can be achieved by switching themicro mirrors on and off rapidly. However, the modes created during thisprocess may not be temporally stable and have the desired intensityprofile only when averaged by a slow detector.

Phase and amplitude information may be encoded by modulating theposition and width of a binary amplitude grating implemented within ahologram such as those illustrated in FIGS. 31A-31H. By implementingsuch holograms to control a DMD, HG modes, LG modes, OAM vortex modes orany angular (ANG) mode may be created by properly programming the DMDwith a hologram. Additionally, the switching between the generated modesmay be performed at a very high speed.

This approach may be realized by considering a one-dimensional binaryamplitude grating. The transmission function for this grating can bewritten as:

${\tau (x)} = {\sum\limits_{n = {- \infty}}^{\infty}{\Pi \lbrack \frac{x - {( {n + k} )x_{0}}}{{wx}_{0}} \rbrack}}$where ${\Pi (v)} = {{{Rect}(v)} = \begin{Bmatrix}1 & {{{if}\mspace{14mu} {v}} \leq 1} \\0 & {else}\end{Bmatrix}}$

This function can be pictured as a pulse train with a period of x₀. Theparameters of “k” and “w” are unitless quantities that set the positionand the width of each pulse and are equal to constant values for auniform grating. It is possible to locally change the value of theseparameters to achieve phase and amplitude modulations of the opticalfield. The transmittance function τ(x) is a periodic function and can beexpanded as a Fourier series.

In a case where k(x) and w(x) are functions of x and the binary gratingis illuminated by a monochromatic plane wave. The first order diffractedlight can be written as:

${\tau_{1}(x)} = {\frac{1}{\pi}{\sin \lbrack {\pi \; {w(x)}} \rbrack}^{{2\pi}\; {k{(x)}}}}$

Thus, w(x) is related to the amplitude of the diffracted light whilek(x) sets its phase. Therefore, the phase and the amplitude of thediffracted light can be controlled by setting the parameters k(x) andw(x). In communication theory, these methods are sometimes referred toas pulse position modulation (PPM) and pulse width modulation (PWM). Theequation above is a good approximation for slowly varying k(x) and w(x)functions.

The above analysis treats a one-dimensional case. A two dimensionalgrating can be generated by thresholding a rapidly varying modulatedcarrier as:

τ(x,y)=½+½sgn{cos [2πx/x ₀ +πk(x,y)]−cos [πw(x,y)]}

Here, sgn(x, y) is the sign function. This may be checked in the limitwhere w(x,y) and k(x,y). One can find the corresponding w(x,y) andk(x,y) functions for a general complex scalar field:

scaler field=A(x,y)e ^(iφ(x,y))

According to the Relations

${w( {x,y} )} = {\frac{1}{\pi}{\sin^{- 1}\lbrack {{{A( {x,y} )}{k( {x,y} )}} = {\frac{1}{\pi}{\phi ( {x,y} )}}} }}$

One could design 2-D binary amplitude holograms to generate LG modes.The gratings holograms designed for vortex modes would have a fairlyuniform width across the aperture whereas for the case of LG modes, thegratings gradually disappear when the amplitude gets negligibly small.

A digital micro-mirror device (DMD) is an amplitude only spatial lightmodulator. The device consist of an array of micro mirrors that can becontrolled in a binary fashion by setting the deflection angle of anindividual mirror to either +12° or −12°. Referring now to FIG. 32A,there is illustrated a general block diagram of a DMD 3202. The DMD 3202includes a plurality of micro-mirrors 3208 arranged in an X by Y array.The array may comprise a 1024×768 array of aluminum micro-mirrors suchas that implemented in the DLP 5500 DMD Array. However, it will beappreciated that other array sizes and DMD devices may be used. Eachmicro-mirror 3208 includes a combination of opto-mechanical andelectro-mechanical elements. Each micro-mirror 3208 comprises a pixel ofthe DMD 3202. The micro-mirror 3208 is an electromechanical elementhaving two stable micro-mirror states of +12° and −12°. Themicro-mirrors have a 10.8 micrometer pitch and are designed for lighthaving a wavelength of 420 nm-700 nm. The state of the micro-mirror 3208is determined by the geometry and electrostatics of the pixel duringoperation. The two positions of the micro-mirror 3208 determine thedirection that the light beam striking the mirror is deflected. Inparticular, the DMD 3202 is a spatial light modulator. By convention,the positive (+) state is tilted toward the illumination and is referredto as the “on” state. Similarly, the negative (−) state is tilted awayfrom the illumination and is referred to as the “off” state.

FIG. 32B illustrates the manner in which a micro-mirror 3208 willinteract with a light source 3230 such as a laser. The light source 3230shines a beam along angle of −24° that strikes the micro-mirror 3208.When the mirror is in the “off” state 3232 at an angle of −12°, the offstate energy 3234 is reflected at an angle of 48°. When the mirror 3208is positioned at the flat state 3236 of 0°, the flat state energy 3238is reflected in an angle of 24°. Finally, when the mirror is at +12° inthe “on” state 3240, the on state energy 3242 is reflected at 0° throughthe projection lens 3244 of a DMD.

Referring now to FIG. 33, there is illustrated a view of the mechanicalstructure of a micro-mirror 3208. The micro-mirror 3208 includes themirror 3302 attached to a torsional hinge 3304 along a diagonal axis3306 of the mirror. The underside of the micro-mirror 3302 makeselectrical contact with the remainder of the circuitry via spring tips3308. A pair of electrodes 3310 is used for holding the micro-mirror3302 in one of the two operational positions (+12° and −12°).

Referring now also to FIG. 34, there is illustrated a block diagram ofthe functional components of the micro-mirror 3208. Below eachmicro-mirror 3208 is a memory cell 3402 consisting of dual CMOS memoryelements 3404. The states of the two memory elements 3404 are notindependent, but are always complementary. If one CMOS memory element3404 is at a logical “1” level, the other CMOS element is at a logical“0” and vice versa. The state of the memory cell 3402 of themicro-mirror 3208 plays a part in the mechanical position of the mirror3208. However, loading information within the memory cell 3402 does notautomatically change the mechanical state of the micro-mirror 3208.

Although the state of the dual CMOS memory elements 3404 plays a part indetermining the state of the micro-mirror 3208, the state of the memoryelements 3304 is not the sole determining factor. Once the micro-mirror3208 has landed, changing the state of the memory cells 3402 will notcause the micro-mirror 3208 to flip to the other state. Thus, the memorystate and the micro-mirror state are not directly linked together. Inorder for the state of the CMOS memory elements 3404 to be transferredto the mechanical position of the micro-mirror 3208, the micro-mirror3108 must receive a “Mirror Clocking Pulse” signal. The mirror clockingpulse signal momentarily releases the micro-mirror 3108 and causes themirror to reposition based on the state of the CMOS memory elements3304. Thus, information relating to mirror positions may be preloadedinto the memory element 3404, and the mechanical position of the mirror3302 for each mirror within a MEMs device 3202 simultaneously changeresponsive to the mirror clocking pulse signal. One manner in which theinformation within the memory cells 3402 may be programmed is throughthe use of holograms, such as those described herein that are used todefined the position of each of the micro-mirrors 3208 with and a MEMsdevice 3202.

When a DMD 3202 is “powered up” or “powered down,” there are prescribedoperations that are necessary to ensure the proper orientation of themicro-mirrors 3208. These operations position the micro-mirrors 3208during power up and release them during power down. The process forchanging the position of a micro-mirror 3208 is more particularlyillustrated in the flowchart of FIG. 35. Initially, at step 3502, thememory states within the memory cells 3402 are set. Once the memorystates have been set within the memory cells 3402, the mirror clockpulse signal may be applied at step 3504. The micro-mirror 3108 willhave an established specification of the time before and after a mirrorclocking pulse that data may be loaded into the memory cell 3402.Application of the mirror clocking pulse signal will then set themirrors to their new state established by the memory at step 3506. Theprocess is completed at step 3508, and the mirror 3302 position is fixedand new data may be loaded into the memory cell 3402.

Referring now to FIG. 36, there is illustrated an intensity and phaseinterferometer for measuring the intensity and phase of the generatedbeam. One can generate spatial modes by loading computer-generatedMatlab holograms 3602 such as those described herein above andillustrated in FIGS. 31A-31H onto a DMD memory. The holograms 3602 forgenerating modes can be created by modulating a grating function with 20micro-mirrors per each period. The holograms 3602 are provided to a DMD3604. An imaging system 3606 along with an aperture 3608 separates thefirst order diffracted light into separate modes. The imaging systemincludes a laser 3610 that provides a light through a pair of lenses3612, 3614. The lens 3612 expands the light beam to lens 3614 whichcollimates the beam. A beam splitter 3616 splits the beam toward a lens3618 and mirror 3621. Lens 3618 focuses the beam through lens 3620 whichcollimates the beam through a filter 3622. The filtered beam isreflected by mirror 3624 through a second beam splitter 3626. The beamsplitter 3626 splits the beam toward a lens 3628 and a charge coupleddevice camera 3630. The charge coupled device (CCD) camera 3630 measuresthe intensity profile of the generated beam. The plane wave beamprovided to lens 3628 is focused on to the aperture 3608 to interferewith the twisted beam from the DMD. Also focused on the aperture 3608 isthe twisted beam from the DMD 3604. The beam from the DMD 3604 isprovided through a lens 3632 that also focuses on the aperture 3608. Thephase of the mode being generated is determined from the number ofspirals in the pattern and is caused by interfering the twisted beamwith a plane wave beam. Also, whether the phase is positive or negativemay be determined by whether the spirals are clockwise (positive) orcounter-clockwise (negative). A Mach-Zehnder interferometer may be usedto verify the phase pattern of the created beams. The collimated planewave provided from lens 3628 is interfered with the modes generated bythe beam from the DMD 3604 through lens 3632. This generates theinterferograms (spiral patterns) at the aperture 3608. The modesgenerated from the DMD may then be multiplexed together usingmemory-based static forks on the DLP.

Therefore, there is a possibility of using binary holograms tocoherently control both phase and amplitude of a light beam. A lownumber of pixels per each period of the binary grating results inquantization errors in encoding phase and intensity. The total number ofgrating periods with in the incident beam on the DMD 3604 sets an upperlimit on the spatial bandwidth of the generated modes. Consequently alarge number of micro-mirrors is preferable for generating high-qualitymodes. This can be achieved by using newer generations of DMDs. Anotherset of modes that are needed for OAM-based quantum key distribution isthe set of angular (ANG) modes.

Referring now to FIG. 37, there is illustrated the manner in whichswitching between different OAM modes may be achieved in real time. Thelaser 3702 generates a collimated beam through lenses 3704 and 3706 to aDMD 3708. The DMD 3708 provides a beam that is focused by lens 3710 ontoaperture 3712. The output from the aperture 3712 is provided to a lens3714 that collimates the beam onto a mirror 3716. The collimated beam isprovided to an OAM sorter 3718 that separates the signal into variousOAM modes 3720 as detected by a computer 3722.

Using DMDs for generating OAM modes provides the ability to switchbetween different modes at very high speeds. This involves a muchsmaller number of optical elements as compared to the conventionaltechniques were OAM modes are generated using a series of separatedforked holograms and are multiplexed using beam splitters. Therefore,one can achieve dynamic switching among vortex OAM modes with differentquantum numbers. The computer-generated holograms for these modes mustbe loaded onto the memory of the DMD 3708, and the switching is achievedby using a clock signal. One can use a mode sorter to map the inputmodes to a series of separated spots. The intensity may then be measuredcorresponding to each mode using a high-bandwidth PIN detector atpositions corresponding to each mode. The DMD devices are available fora fraction of the cost of phase only spatial light modulators.

The DMD efficiency observed in a specific application depends onapplication-specific design variables such as illumination wavelength,illumination angle, projection aperture size, overfill of the DMDmicro-mirror array and so on. Overall optical efficiency of each DMD cangenerally be estimated as a product of window transmission, adiffraction efficiency, micro-mirror surface reflectivity and array fillfactor. The first three factors depend on the wavelength of theillumination source.

DLP technology uses two types of materials for DMD mirrors. The mirrormaterial for all DMD's except Type-A is Corning Eagle XG, whereas type ADMDs use Corning 7056. Both mirror types have an anti-reflectivity (AR),thin-film coating on both the top and the bottom of the window glassmaterial. AR coatings reduce reflections and increase transmissionefficiency. The DMD mirrors are designed for three transmission regions.These ranges include the ultraviolet light region from 300 nm to 400 nm,the visible light region from 400 nm to 700 nm and the near infraredlight region (NIR) from 700 nm to 2500 nm. The coating used depends onthe application. UV windows have special AR coatings designed to be moretransmissive for ultraviolet wavelengths, visible coatings for visibleDMDs and NIR coatings for NIR DMDs.

The measured data provided in the following sections reflects a typicalsingle pass transmittance through both top and bottom AR coated mirrorsurfaces with random polarization. The angle of incidence (AOI) of 0° ismeasured perpendicular to the window surface unless mentioned otherwise.With an increase in the number of window passes, the efficiency woulddecline.

FIG. 38 represents the window transmission curves for Corning 7056. Thewindow transmission response curve in this figure applies to TaipeiMDM's in their specified illumination wavelength regions. FIG. 38 showsthe UV window transmittance measured perpendicular to the window surfaceand visible window transmittance at a lie of 0° and 30°. FIGS. 39-43 arezoomed in views of the typical visible and UV AR coated windowtransmittance in their maximum transmission regions. The visible CorningEagle XG window transmission data shown in FIG. 42 applies to the DLP5500, DLP 1700, DLP 3000 and DLP 3000 DMD's. The typical transmittanceobserved in these DMD's is broadband visible region is approximately97%. The NIR Corning Eagle XG window transmission data of FIG. 43applies to the DLP 3000 NIR DMD. The typical transmittance observed inthe NIR DMD's in the broadband NIR region is approximately 96% for mostof the region with a dip toward 90% as it nears 2500 nm.

Referring now to FIG. 44, there is illustrated a configuration ofgeneration circuitry for the generation of an OAM twisted beam using ahologram within a micro-electrical mechanical device. A laser 4402generates a beam having a wavelength of approximately 543 nm. This beamis focused through a telescope 4404 and lens 4406 onto a mirror/systemof mirrors 4408. The beam is reflected from the mirrors 4408 into a DMD4410. The DMD 4410 has programmed in to its memory a one or more forkedholograms 4412 that generate a desired OAM twisted beam 4413 having anydesired information encoded into the OAM modes of the beam that isdetected by a CCD 4414. The holograms 4412 are loaded into the memory ofthe DMD 4410 and displayed as a static image. In the case of 1024×768DMD array, the images must comprise 1024 by 768 images. The controlsoftware of the DMD 4410 converts the holograms into .bmp files. Theholograms may be displayed singly or as multiple holograms displayedtogether in order to multiplex particular OAM modes onto a single beam.The manner of generating the hologram 4412 within the DMD 4410 may beimplemented in a number of fashions that provide qualitative differencesbetween the generated OAM beam 4413. Phase and amplitude information maybe encoded into a beam by modulating the position and width of a binaryamplitude grating used as a hologram. By realizing such holograms on aDMD the creation of HG modes, LG modes, OAM vortex mode or any angularmode may be realized. Furthermore, by performing switching of thegenerated modes at a very high speed, information may be encoded withinthe helicity's that are dynamically changing to provide a new type ofhelicity modulation. Spatial modes may be generated by loadingcomputer-generated holograms onto a DMD. These holograms can be createdby modulating a grating function with 20 micro mirrors per each period.

Rather than just generating an OAM beam 4413 having only a single OAMvalue included therein, multiple OAM values may be multiplexed into theOAM beam in a variety of manners as described herein below. The use ofmultiple OAM values allows for the incorporation of differentinformation into the light beam. Programmable structured light providedby the DLP allows for the projection of custom and adaptable patterns.These patterns may be programmed into the memory of the DLP and used forimparting different information through the light beam. Furthermore, ifthese patterns are clocked dynamically a modulation scheme may becreated where the information is encoded in the helicities of thestructured beams.

Referring now to FIG. 45, rather than just having the laser beam 4502shine on a single hologram multiple holograms 4504 may be generated bythe DMD 4410. FIG. 45 illustrates an implementation wherein a 4×3 arrayof holograms 4504 are generated by the DMD 4410. The holograms 4504 aresquare and each edge of a hologram lines up with an edge of an adjacenthologram to create the 4×3 array. The OAM values provided by each of theholograms 4504 are multiplexed together by shining the beam 4502 ontothe array of holograms 4504. Several configurations of the holograms4504 may be used in order to provide differing qualities of the OAM beam4413 and associated modes generated by passing a light beam through thearray of holograms 4504.

Referring now to FIG. 46 there is illustrated an alternative way ofmultiplexing various OAM modes together. An X by Y array of holograms4602 has each of the hologram 4602 placed upon a black (dark) background4604 in order to segregate the various modes from each other. In anotherconfiguration illustrated in FIG. 47, the holograms 4702 are placed in ahexagonal configuration with the background in the off (black) state inorder to better segregate the modes.

FIG. 48 illustrates yet another technique for multiplexing multiple OAMmodes together wherein the holograms 4802 are cycled through in a loopsequence by the DMD 4410. In this example modes T₀-T₁₁ are cycledthrough and the process repeats by returning back to mode T₀. Thisprocess repeats in a continuous loop in order to provide an OAM twistedbeam with each of the modes multiplex therein.

In addition to providing integer OAM modes using holograms within theDMD, fractional OAM modes may also be presented by the DMD usingfractional binary forks as illustrated in FIG. 49. FIG. 49 illustratesfractional binary forks for generating fractional OAM modes of 0.25,0.50, 0.75, 1.25, 1.50 and 1.75 with a light beam.

Referring now to FIG. 50-63, there are illustrated the results achievedfrom various configurations of holograms program within the memory of aDMD. FIG. 50 illustrates the configuration at 5002 having no hologramseparation on a white background producing the OAM mode image 5004. FIG.51 uses a configuration 5102 consisting of circular holograms 5004having separation on a white background. The OAM mode image 5006 that isprovided therefrom is also illustrated. Bright mode separation yieldsless light and better mode separation.

FIG. 52 illustrates a configuration 5202 having square holograms with noseparation on a black background. The configuration 5202 generates theOAM mode image 5204. FIG. 53 illustrates the configuration of circularholograms (radius ˜256 pixels) that are separated on a black background.This yields the OAM mode image 5304. Dark mode separation yields morelight in the OAM image 5304 and has slightly better mode separation.

FIG. 54 illustrates a configuration 5402 having a bright background andcircular hologram (radius ˜256 pixels) separation yielding an OAM modeimage 5404. FIG. 55 illustrates a configuration 5502 using circularholograms (radius ˜256 pixels) having separation on a black backgroundto yield the OAM mode image 5504. The dark mode separation yields morelight and has a slightly worse mode separation within the OAM modeimages.

FIG. 56 illustrates a configuration 5602 including circular holograms(radius ˜256 pixels) in a hexagonal distribution on a bright backgroundyielding an OAM mode image 5604. FIG. 57 illustrates at 5702 smallcircular holograms (radius ˜256 pixels) in a hexagonal distribution on abright background that yields and OAM mode image 5704. The largerholograms with brighter backgrounds yield better OAM mode separationimages.

Referring now to FIG. 58, there is illustrated a configuration 5802 ofcircular holograms (radius ˜256 pixels) in a hexagonal distribution on adark background with each of the holograms having a radius ofapproximately 256 pixels. This configuration 5802 yields the OAM modeimage 5804. FIG. 59 illustrates the use of small holograms (radius ˜256pixels) having a radius of approximately 190 pixels arranged in ahexagonal distribution on a black background that yields the OAM modeimage 5904. Larger holograms (radius of approximately 256 pixels) havinga dark background yields worse OAM mode separation within the OAM modeimages.

FIG. 60 illustrates a configuration 6002 of small holograms (radius ofapproximately 190 pixels) in a hexagonal separated distribution on adark background that yields the OAM mode image 6004. FIG. 61 illustratesa configuration 6102 of small holograms (radius ˜256 pixels) in ahexagonal distribution that are close together on a dark background thatyields the OAM mode image 6104. The larger dark boundaries (FIG. 60)yield worse OAM mode image separation than a smaller dark boundary.

FIG. 62 illustrates a configuration 6202 of small holograms (radius ˜256pixels) in a separated hexagonal configuration on a bright backgroundyielding OAM mode image 6204. FIG. 63 illustrates a configuration 6302of small holograms (radius ˜256 pixels) more closely spaced in ahexagonal configuration on a bright background yielding OAM mode image6304. The larger bright boundaries (FIG. 62) yield a better OAM modeseparation.

Additional illustrations of holograms, namely reduced binary hologramsare illustrated in FIGS. 64-67. FIG. 64 illustrates reduced binaryholograms having a radius equal to 100 micro mirrors and a period of 50for various OAM modes. Similarly, OAM modes are illustrated for reducedbinary for holograms having a radius of 50 micro mirrors and a period of50 (FIG. 65); a radius of 100 micro mirrors and a period of 100 (FIG.66) and a radius of 50 micro mirrors and a period of 50 (FIG. 67).

The illustrated data with respect to the holograms of FIGS. 50-67demonstrates that full forked gratings yield a great deal of scatteredlight. Finer forked gratings yield better define modes within OAMimages. By removing unnecessary light from the hologram (white regions)there is a reduction in scatter. Holograms that are larger and havefewer features (more dark zones) having a hologram diameter of 200 micromirrors provide overlapping modes and strong intensity. Similarconfigurations using 100 micro mirrors also demonstrate overlappingmodes and strong intensity. Smaller holograms having smaller radiibetween 100-200 micro mirrors and periods between 50 and 100 generatedby a DLP produce better defined modes and have stronger intensity thanlarger holograms with larger radii in periods. Smaller holograms havingmore features (dark zones with hologram diameters of 200 micro mirrorsprovide well-defined modes with strong intensity. However, hundred micromirror diameter holograms while providing well-defined modes provideweaker intensity. Thus, good, compact hologram sizes are between 100-200micro mirrors with zone periods of between 50 and 100. Larger hologramshave been shown to provide a richer OAM topology.

Additional methods of providing multimode OAM generation by implementingmultiple holograms within a MEMs device are illustrated in FIG. 68.These configurations of holograms illustrate the hologram configurationsand associated OAM mode images for mode combinations from l=1 to l=1, 2,3, 4, 5, 6, 7.

In addition to the binary forked holograms discussed hereinabove, theMatlab capability of the DMD also enables the generation of binaryspiral holograms of differing mode levels. FIG. 69 illustrates binaryspiral holograms for l=1 and l=20.

It will be appreciated by those skilled in the art having the benefit ofthis disclosure that this system and method for applying orthogonallimitations to light beams using microelectromechanical systems providesimproved mode data transmission capability. It should be understood thatthe drawings and detailed description herein are to be regarded in anillustrative rather than a restrictive manner, and are not intended tobe limiting to the particular forms and examples disclosed. On thecontrary, included are any further modifications, changes,rearrangements, substitutions, alternatives, design choices, andembodiments apparent to those of ordinary skill in the art, withoutdeparting from the spirit and scope hereof, as defined by the followingclaims. Thus, it is intended that the following claims be interpreted toembrace all such further modifications, changes, rearrangements,substitutions, alternatives, design choices, and embodiments.

1. A system for generating a light beam having a plurality of orbitalangular momentum modes applied thereto, comprising: a light source forgenerating a plane wave light beam; a MicroElectroMechanical (MEM)system including an array of micro-mirrors for generating the light beamhaving the plurality of orbital angular momentum modes applied theretoresponsive to the plane wave light beam and control signals forcontrolling the array of micro-mirrors; a controller for generating thecontrol signals to control a position of each of a plurality ofmicro-mirrors of the array of micro-mirrors; and wherein the controllercontrols the position of the micro-mirrors to generate a plurality ofholograms for applying the plurality of orbital angular momentum modesto the plane wave light beam responsive to the control signals.
 2. Thesystem of claim 1, wherein the controller switches the array ofmicro-mirrors between different holograms to dynamically controlhelicities applied to the light beam from the MEM system.
 3. The systemof claim 1, wherein the controller controls the array of micro-mirrorsto produce holograms having a radius substantially in a range of 100-200micro-mirrors and a period substantially in a range of 50-100.
 4. Thesystem of claim 1 further including a memory for storing data enablingthe controller to generate the plurality of holograms responsive to thedata.
 5. The system of claim 1, wherein the light beam comprises a lightbeam in frequencies in a range from infra-red to ultra-violet.
 6. Thesystem of claim 1, wherein the MEM system further comprises switchingcircuitry responsive to the control signals for switching micro-mirrorswithin the array of micro-mirrors between an “on” state and an “off”state at least 1000 times per second.
 7. The system of claim 1, whereinthe controller configures the array of micro-mirrors to present aplurality of holograms at a same time.
 8. The system of claim 7, whereinthe controller configures the array of micro-mirrors to selectivelypresent the plurality of hologram on a light background or a darkbackground.
 9. The system of claim 7, wherein the controller configuresthe array of micro-mirrors to present the plurality of holograms with aseparation between each of the holograms.
 10. A system for generating alight beam having a plurality of orthogonal function modes appliedthereto, comprising: a light source for generating a plane wave lightbeam; a MicroElectroMechanical (MEM) system including an array ofmicro-mirrors for generating the light beam having the plurality oforthogonal function modes applied thereto responsive to the plane wavelight beam and control signals for controlling the array ofmicro-mirrors; a controller for generating the control signals tocontrol a position of each of a plurality of micro-mirrors of the arrayof micro-mirrors; and wherein the controller controls the position ofthe micro-mirrors to generate a plurality of holograms for applying theplurality of orbital angular momentum modes to the plane wave light beamresponsive to the control signals.
 11. The system of claim 10, whereinthe controller switches the array of micro-mirrors between differentholograms to dynamically control the orthogonal functions applied to thelight beam from the MEM system.
 12. The system of claim 10, wherein thecontroller controls the array of micro-mirrors to produce hologramshaving a radius substantially in a range of 100-200 micro-mirrors and aperiod substantially in a range of 50-100.
 13. The system of claim 10further including a memory for storing data enabling the controller togenerate the plurality of holograms responsive to the data.
 14. Thesystem of claim 10, wherein the light beam comprises a light beam infrequencies in a range from infra-red to ultra-violet.
 15. The system ofclaim 10, wherein the MEM system further comprises switching circuitryresponsive to the control signals for switching micro-mirrors within thearray of micro-mirrors between an “on” state and an “off” state at least1000 times per second.
 16. The system of claim 10, wherein thecontroller configures the array of micro-mirrors to present a pluralityof holograms at a same time.
 17. The system of claim 16, wherein thecontroller configures the array of micro-mirrors to selectively presentthe plurality of hologram on a light background or a dark background.18. The system of claim 16, wherein the controller configures the arrayof micro-mirrors to present the plurality of holograms with a separationbetween each of the holograms.
 19. The system of claim 10, wherein theorthogonal function modes further comprises one of Laguerre-Gaussianfunctions, Hermite-Gaussian functions or twisted mode functions.
 20. Thesystem of claim 10, wherein the light beam having the plurality oforthogonal function modes applied thereto is used for quantum keydistribution.
 21. A method for generating a light beam having aplurality of orthogonal function modes applied thereto, comprising:generating a plane wave light beam; generating, using aMicroElectroMechanical (MEM) system including a plurality ofmicro-mirrors, the light beam having the plurality of orthogonalfunction modes applied thereto responsive to the plane wave light beamand control signals for controlling the array of micro-mirrors, whereinthe step of generating the light beam having the plurality of orthogonalfunction modes applied thereto further comprises: generating, using acontroller of the MEM system, the control signals to control a positionof each of a plurality of micro-mirrors of the array of micro-mirrors;configuring the position of the micro-mirrors to generate a plurality ofholograms responsive to the control signals; and applying the pluralityof orbital angular momentum modes to the plane wave light beam using theholograms to encode data therein.
 22. The method of claim 21, whereinthe step of configuring further comprises switching the array ofmicro-mirrors between different holograms to dynamically control theorthogonal functions applied to the light beam.
 23. The method of claim21, wherein the step of configuring further comprises configuring theposition of micro-mirrors to produce holograms having a radiussubstantially in a range of 100-200 micro-mirrors and a periodsubstantially in a range of 50-100.
 24. The method of claim 21 furtherincluding storing, within a memory associated with the MEM system, dataenabling the controller to generate the plurality of hologramsresponsive to the data.
 25. The method of claim 21, wherein the step ofgenerating a plane wave light beam further comprise generating the planewave light beam in a frequency in a range from infra-red toultra-violet.
 26. The method of claim 21, wherein the step ofconfiguring further comprises switching micro-mirrors within the arrayof micro-mirrors between an “on” state and an “off” state a plurality oftimes per second.
 27. The method of claim 21, wherein the step ofconfiguring further comprises configuring the micro-mirrors of the arrayof micro-mirrors to present a plurality of holograms at a same time. 28.The method of claim 27, wherein the step of configuring furthercomprises configuring the micro-mirrors of the array of micro-mirrors toselectively present the plurality of hologram at the same time on alight background or a dark background.
 29. The method of claim 27,wherein the step of configuring further comprises configuring themicro-mirrors of the array of micro-mirrors to present the plurality ofholograms at the same time with a separation between each of theholograms.
 30. The method of claim 21, wherein the orthogonal functionmodes further comprises one of Laguerre-Gaussian functions,Hermite-Gaussian functions or twisted mode functions.